NXB i hc Quc gia H Ni 2003

T kho: Sai s, nh l, ngn hn, hn di, trung hn, mc nc, lu lng,

ma - dng chy, m hnh ton, tt nh, ngu nhin, kinh nghim

Ti liu trong Th vin in t i hc Khoa hc T nhin c th c s

dng cho mc ch hc tp v nghin cu c nhn. Nghim cm mi hnh

thc sao chp, in n phc v cc mc ch khc nu khng c s chp

thun ca nh xut bn v tc gi.

D BO THY VN

Nguyn Vn Tun - on Quyt Trung - Bi Vn c

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Nguyn Vn Tun - on Quyt Trung - Bi Vn c

GIO TRNH

D BO THU VN

NH XUT BN I HC QUC GIA H NI

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MC LC LI NI U ................................................................................................. 6 Chng 1. KHI QUT CHUNG V D BO THU VN. .................. 7

1.1. D bo thy vn - Mt phn ca thu vn hc................................. 7 1.2. S lc lch s pht trin ca d bo thu vn................................ 9

1.2.1. S lc lch s pht trin d bo thu vn ngoi nc. ............. 9 1.2.2 .S lc lch s pht trin d bo thu vn Vit Nam. .............. 12

1.3. Vai tr ca d bo thy vn trong khai thc v qun l ngun nc. ........................................................................................................... 19

1.3.1. Phc v thi cng v khai thc cng trnh thu in vi mc tiu an ton, vn hnh ti u, hiu ch kinh t cao. ............................................ 20 1.3.2- Phc v ti tiu: p ng cc yu cu ti nc phng hn, tiu nc chng ng, tham gia iu tit cc h cha v m bo an ton cho cc cng trnh thu li trn ton quc..................................................... 21 1,3,3, D bo thu vn phc v giao thng ng thu......................... 21 1.3.4. D bo thy vn phc v cc h thng thu nng........................ 22

1.4. D bo thu vn phc v chng thin tai, l lt ............................. 22 1.5. Phn loi d bo thu vn................................................................. 23

1.5.1- Phn loi d bo thu vn theo hin tng .................................. 23 1.5.2- Phn loi theo quy lut chuyn ng nc................................... 23 1.5.3- Phn loi theo thi gian d kin ................................................... 24

1.6. Mt vi khi nim quan trng .......................................................... 24 1.6.1 Phng php v phng n: .......................................................... 24 1.6.2- Cc bc tin hnh xy phng n d bo .................................. 25

1.7. nh gi chnh xc v bo m d bo thu vn ................ 26 1.8 nh gi phng n d bo............................................................... 27

Chng 2. H PHNG TRNH DNG KHNG N NH SAINT VENANT ........................................................................................................ 31

2.1. Cc dng chuyn ng ca cht lng trong knh h...................... 31 2.1.1. Dng n nh................................................................................. 31 2.1.2. Chuyn ng khng n nh ......................................................... 32

2.2. Phng trnh vi phn c bn ca dng khng n nh thay i chm............................................................................................................ 32

2.2.1. Phng trnh lin tc..................................................................... 32 2.2.2. Phng trnh cn bng ng lc ca dng khng n nh ........... 33 2.2.3. Phn loi m hnh din ton phn phi......................................... 35 2.2.4. Nm gi thit ca phng trnh .................................................... 37

2.3 Xp x ca sai phn (Sai phn ha) ................................................... 37 2.3.1. Khi nim chung ........................................................................... 37 2.3.2- Phng php sai phn................................................................... 38 2.3.3 H s trng lng ca s n...................................................... 44

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2.3.4 Phng trnh c bn vit vi hm s n Q,Z trong trng hp tng qut. ......................................................................................................... 44 2.3.5 S sai phn n ........................................................................... 48 2.3.6 Cch gii bng kh ui ................................................................ 57

2.4. S lc v hi t v s n nh ca nghim .................................... 61 2.5 S sai phn hin tnh ton cho knh h. ...................................... 63

2.5.1. S v cng thc c bn. ........................................................... 63 2.5.3 Vn xc nh iu kin ban u . .............................................. 71

Chng 3. D BO CHUYN NG SNG L V PHNG PHP MC NC TNG NG............................................................ 76

3.1 Khi nim v phng php mc nc tng ng. ...................... 76 3.2 . L thuyt chuyn ng sng l v phng php mc nc tng ng .............................................................................................................. 76 3.3. Xc nh thi gian chy truyn......................................................... 79

3.3.1 Thi gian chy truyn l thi gian chy t mt ct thng lu (Hb) ti mt ct cn xc nh h lu (HH) .................................................... 79 3.3.2. Tm 1 c th t cng thc (3.13), c th xy dng bng sau: .... 79 3.3.3- Tm t cng thc tc mt ct ngang VQ................................ 80

3.4- D bo mc nc trn sng khng hoc t sng nhnh................. 81 3.5 D bo mc nc trn sng c sng nhnh...................................... 83

Chng 4. D BO LU LNG GN NG BNG CHUYN NG SNG L .......................................................................................... 88

4.1. Phng php dng khng n nh ca Kalinin - Miliukop ........... 88 4.2 Phng php bin dng l - Phng php Muskingum................. 94 4.3 Phng php din ton l- M hnh SSARR. ................................. 96

Chng 5. D BO MA DNG CHY TRN H THNG SNG. 99 5.1 Cng thc cn nguyn dng chy..................................................... 99 5.2. Nhng yu t hnh thnh dng chy. ............................................. 102 5.3. Cc phng php d bo dng chy t ma ................................ 104

5.3.1.Phng php quan h ma- nh l : ........................................... 104 5.3.2 Xy dng quan h tng quan hp trc....................................... 105 5.3.3 K thut m hnh.......................................................................... 105 5.3.4 M hnh ma - dng chy ba tng ............................................... 108

5.4 Bi tp................................................................................................. 112 Chng 6. D BO DNG CHY PHC V H CHA CNG TRNH THU IN .................................................................................. 114

6.1 Hnh nh chung ca cng trnh thu in v ti liu kh tng thu vn c lin quan. ...................................................................................... 114

6.1.1 Loi ti liu a l t nhin ca lu vc v h cha.................... 114 6.1.2 Loi ti liu kh tng thu vn................................................... 116 6.1.3 Tin thi cng ........................................................................... 116 6.1.4. Cng tc vn hnh h cha ......................................................... 117

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6.2 Nhng yu cu ca h cha, nh my thu in i vi d bo thu vn.................................................................................................... 117

6.2.1. Giai on dn dng thi cngbc mt ........................................ 117 6.2.2. Giai on ngn dng (hp long) (t hai)................................... 118 6.2.3 Giai on vn hnh cng trnh thu in ..................................... 122

6.3 . C s v phng php d bo thu vn cho h cha ................. 125 6.3.1.C s ca phng php................................................................ 126 6.3.2. Cc phng php d bo h cha .............................................. 127 6.3.3 Phng php d bo sng trn h................................................ 133 6.3.4 Phng php phc hi dng chy n h .................................... 134

Chng 7. D BO TRUNG V DI HN............................................ 139 7.1 Khi nim chung v d bo trung v di hn ................................ 139

7.1.1. Khi nim chung ......................................................................... 139 7.1.2. Hnh thc pht bo ca d bo trung di hn. ........................... 139

7.2. Phng php d bo trung v di hn .......................................... 140 7.2.1 Phng trnh cn nguyn .......................................................... 140 7.2.2 Cc nhn t nh hng............................................................. 141

7.3 Cc phng php d bo truyn thng......................................... 145 7.3.1 D bo dng chy thng theo ch s lng tr ......................... 145 7.3.2 D bo dng chy thng theo ch s lng tr ban u v ma trong thng ............................................................................................ 146 7.3.3 D bo dng chy thng theo cc thnh phn cn nguyn....... 147

7.4 Mt s phng php thng k trong d bo kh tng thu vn................................................................................................................... 150

7.4.1 Phn tch chui thi gian............................................................. 150 7.4.2 Cc phng php vt l thng k .............................................. 155 7.4.3. Mt s nhn xt v nh hng ng dng ................................. 169

7.5 Cng ngh d bo.............................................................................. 170 7.5.1 Khi nim chung. ......................................................................... 170 7.5.2 C s d liu ................................................................................ 171 7.5.3 M t cng ngh........................................................................... 173 7.5.4 Hng dn s dng ................................................................... 176 7.5.5 Mt s nhn xt v kt lun ......................................................... 177

Chng 8. NG DNG VIN THM D BO L. ............................. 178 8.1 Gii thiu chung v cu trc m hnh d bo l bng vin thm.178 8.2. H thng my o ma truyn thng quan trc dng chy. ......... 178 8.3. Vai tr ca vin thm trong h thng d bo l. .......................... 182 8.4. S dng v tinh raa d bo l. ................................................ 185 8.5. Nguyn l o lng ma bng ra a .............................................. 186

8.5.1. Nhng sai s xut hin khi dng raa, c im v v tr t raa................................................................................................................ 188 8.5.2. Nhng sai s xut hin t s s dng raa. ................................ 190

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8.5.3- S dng raa theo di ng i ca bo. .............................. 191 8.5.4- Mc sai s khi dng s liu raa. .......................................... 191 8.5.5- S cn thit vic s dng raa kt hp vi cc s liu quan trc cc trm o. ........................................................................................... 192

8.6- H thng truyn pht tn hiu t xa dng cho d bo dng chy.................................................................................................................... 193

8.6.1- Gii thiu. ................................................................................... 193 8.6.2- H thng ng dy in thai................................................... 193 8.6.3- Sng radio (sng v tuyn in)................................................. 194 8.6.4- H thng thu pht Meteor Burst. ................................................ 194 8.6.5 Truyn pht thng tin bng v tinh. ............................................. 195

8.7- Kh tng v d bo hnh th Sy np. ........................................... 199 8.7.1- Gii thiu. ................................................................................... 199 8.7.2- K thut d bo thi tit. ............................................................ 199 8.7.3- S dng v tinh trong d bo hnh th Sy np .......................... 200

Chng 9. D BO MC NC NGM V DNG CHY NGM.202 9.1 C s chung ca d bo.................................................................... 202 9.2- D bo bng phng php cn bng nc ................................... 208 9.3 D bo bng phng php ng lc hc nc ngm.................... 210 9.4 Cc phng php d bo thng k. ................................................ 216

TI LIU THAM KHO. ...................................................................... 218 PREPACE. ................................................................................................... 220

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LI NI U

p ng nhu cu nng cao cht lng o to sinh vin trng i hc Quc gia vic vit gio trnh D bo thu vn l mt nhu cu bc thit.

Gio trnh D bo thu vn ra i nhm cung cp cho sinh vin kin thc c bn v cc khi nim, yu cu thc t i vi d bo thu vn, cc c s l thuyt ca cc phng php d bo thu vn trong c h thng phng trnh Saint- Venant, cc phng php c bn, c truyn v cp nht cc phng php hin i- thu vn ton dng trong d bo thu vn. hc tt mn ny sinh vin cn nm cc kin thc c bn v thu lc hc, kh tng hc, mt s kin thc v ton cn thit nh l thuyt xc sut thng k, phng trnh vi phn, phng php tnh v k thut lp trnh.

Gio trnh ny dng cho sinh vin chuyn ngnh thu vn lc a, cc k s thu vn lm vic cc trung tm d bo v cc u ban phng chng l lt khai thc ti nguyn nc. Ngoi ra cn c th dng cho sinh vin cao hc.

Gio trnh ny c hon thnh do cc thy gio, cc nh khoa hc lm vic nhiu nm trong d bo tc nghip trung tm d bo kh tng thu vn quc gia.

PGS- PTS Nguyn Vn Tun vit chng I, VI, VIII, IX v l ngi ch bin gio trnh ny.

PGS- PTS on Quyt Trung vit chng II, III, IV, V. PTS Bi Vn c vit chng VII. y l gio trnh ln u tin c bin son v xut bn do khng

trnh khi sai st, khim khuyt. Rt mong nhn c s ng gp ca c gi. Xin chn thnh cm n!

Cc tc gi.

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Chng 1. KHI QUT CHUNG V D BO THU VN.

1.1. D bo thy vn - Mt phn ca thu vn hc. T d bo bt ngun t hai t La tinh l pha trc v gi tr. V th d bo c ngha l on trc s pht trin hoc mt i ca mt hin tng no . D bo thu vn l bo trc mt cch c khoa hc trng thi (tnh hnh) bin i cc yu t thu vn sng, sui, h nh lng nc, mc nc. D bo thu vn l mt mn khoa hc- l hc thuyt v vic bo trc s xut hin (pht sinh) pht trin cc yu t thu vn trn c s nghin cu cc quy lut ca chng. Mc ch ch yu ca n l tm ra nhng phng php d bo dng chy, mc nc, lu lng nc sng v cc hin tng khc trong sng ngi v h. Bn thn vic nghin cu cc hin tng ny thuc v mn khoa hc khc: thu vn lc a. Mc d vy cc nh khoa hc lm cng tc d bo vn rt ch trng nghin cu cc quy lut pht trin ca cc yu t d bo. H khng nhng tin hnh cc phn tch l thuyt m cn tin hnh quan trc v th nghim trn cc bi thc nghim ca cc trm cn bng nc. Trong qu trnh nghin cu cc phng php d bo, h sng lp ra cc thuyt gn ng v chuyn ng sng l, nghin cu ng lc hc lng tr nc trong li sng, c nhng ng gp ng k vo vic gii quyt vn hnh thnh dng chy trn sn dc. Trong vic tin hnh cc nghin cu trn cng nh trong vic tm ra nhng phng php d bo c th m hnh ton ng mt vai tr quan trng. M hnh ton l mt cng c nghin cu khoa hc bao gm c h thng tru tng ( ngh) v h thng vt l (vt cht) phn nh hoc ti hin li cc hin tng hoc qu trnh ang nghin cu. Chng cho php thu nhn c lng thng tin cn thit hiu su hn cc hin tng , hoc nhng ghi chp nh lng cc qu trnh . Trong mt s trng hp m hnh cho php

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chng ta trc tip xy dng cc hc thuyt, cn nhng trng hp khc - c th ho cc hc thuyt di dng gii nhng bi ton c th. Nh nhng thc nghim bng s m hnh cho php chng ta nghin cu s tng tc gia cc yu t khc nhau v thu c nhng khi nim khch quan v cc mi lin quan , hoc nhng s n gin c th s dng nghin cu cc phng php d bo p dng cho trng hp s liu quan trc thc t t. M hnh cn gip chng ta xc nh s liu quan trc b sung cn thit v nh gi chnh xc ca cc d bo theo chnh xc ca s liu s dng. Cui cng, bng cch s dng cc s liu quan trc chng ta c th kt lun c mc ph hp ca m hnh chn vi thc t khch quan m t ta xy dng m hnh. Khng him trng hp m hnh ho c hiu nh s phn tch h thng v gii nh my tnh in t, nhng bi ton phc tp c s dng ti u ho cc thng s. i khi phn tch h thng nh mt phng php nghin cu li c i lp vi nhng phng php phn tch vt l phn tch v tng hp thng thng. Mt s i lp nh th tt nhin khng th coi l ng v phn tch h thng khng th t pht trin tch ri khi phn tch vt l, cn s l gii kt qu ca n th hon ton ph thuc vo s hiu bit ng n cc qu trnh vt l tng ng. Mc d vic phn tch cn nguyn v m hnh ho trong vic tm ra nhng phng php d bo quan trng nh vy, kt qu thc t ca cc cuc tm ti vn ph thuc vo s c mt ca cc s liu quan trc thc t, tnh i biu, chnh xc v y ca chng.

Chng ta bit rng trong qu trnh tn ti dng chy chu nh hng ca rt nhiu yu t k c yu t a l t nhin (cht t, lp ph thc vt...) Tnh bin ng cao ca cc yu t ny theo khng gian v thi gian gy nn kh khn ln trong vic thnh lp cc phng php cht ch tnh ton trong sng. iu lm cho mi phng php d bo ch c th l mt cch gii gn ng bi ton. D bo thu vn -mt trong nhng phn kh ca thy vn hc.

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1.2. S lc lch s pht trin ca d bo thu vn.

1.2.1. S lc lch s pht trin d bo thu vn ngoi nc.

-S pht trin ca mn d bo thu vn gn b cht ch vi nhng i hi thc t. Yu cu v d bo l lt dn ti s xut hin nhng cng trnh u tin trong lnh vc ny.

D bo thu vn ca Vit Nam gn vi s pht trin ch thu vn ca Lin X c.

Vo nhng nm 90 ca th k trc V.G.Clyber, D.D.Gnuxin v A.N.Crisinxki thnh lp c nhng phng php u tin d bo ngn hn mc nc cc sng ng thu ca nc Nga. Vic d bo mc nc c tin hnh da trn qui lut chuyn ng ca nc trong lng sng. Trong khi d bo ngi ta ch s dng mc nc sng ti tuyn trn.

Trong s nhng cng trnh nghin cu trc cch mng thng 10 cn ghi nhn y cng trnh ca E.M.Onecp trong xt ti mi quan h gia dng chy cc sng min ni vng Trung v lng ma. Cng trnh ny c mang tnh cht d bo r rt.

Sau cch mng thng 10 Nga: nm 1919 Vin thu vn Lin X (nay l Vin quc gia) c thnh lp v bt u tin hnh nghin cu c h thng ch thu vn cc sng, h, m ly v ngun ti nguyn nc. Vic thnh lp Vin trong nhng nm m nh nc X Vit tr tui ang phi tin hnh cuc chin tranh i quc chng t s ch c bit ca Lnin V.I v chnh quyn X Vit ti trin vng s dng ti nguyn nc.

Cng vi s thnh lp Vin thu vn quc gia vic nghin cu d bo thu vn c bt u. Lch s pht trin ca d bo thu vn c th chia thnh 3 giai on: c-T 1919 n gia nhng nm 30, d-T gia nhng nm 30 n gia nhng nm 40, e-T gia nhng nm 40 n nay.

-c trng ca giai on c l gii quyt mt s nhim v d bo bng cch thnh lp cc tng quan thc nghim thun tu. V d nh tng quan

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gia cao l ma xun, dng chy vi cc yu t m thi cho rng c nh hng quyt nh ti yu t d bo. Nhng cng trnh ny em li nhng li ch hin nhin. N dn ti mt s cc phng php d bo thc hnh v thc y vic l gii cc iu kin v nhn t hnh thnh l v cc hin tng khc. Giai on ny cn c c trng bi s s dng rng ri phng php tng quan tuyn tnh (bao gm c tng quan nhiu chiu). Cn phi k ra y cc cng trnh nghin cu ca L.N.avp, B.A.Aplp, A.V.Oghiepski, O.T.Maskvich, P.N.Nasukp, V.N.Lbep.

Nm 1924 L.avp xut bn cun sch cp n hai vn : d bo dng chy cho cc sng min ni v vic t chc nghnh d bo thu vn Trung .

T nm 1929 Tng cc kh tng thu vn Lin X c thnh lp. Mt trong nhng nhim v ca Tng cc l cung cp cc thng tin v trng thi ca sng h, hin ti v tng lai, cho nn kinh t quc dn v dn c. T cc phng d bo thu vn thuc cc i kh tng thu vn cng c thnh lp. B phn d bo thu vn ca Cc d bo trung ng Maxtcva tr thnh trung tm lnh o v khoa hc v phng php lun khoa hc.

Nhng nghin cu u tin v thu vn mang tnh cht ng dng. Nh sm xut hin kh nng xy dng cc nh my thu in Vnkhpxkaia v Donhp. Nhng im u tin trong k hoch GOENRO- cc thng bo thu vn u tin trong lch s t nc c thnh lp di s lnh o ca N.V.Lbep v A.V.Oghiepxki.

- Nhng c trng c bn ca giai on pht trin th hai l vic s dng phng php cn bng nc vo nghin cu thu vn (cng trnh ca .A.Aplp, G.F.Kalinin, V.B.Kmarp, N.I.Lvp v nhiu tc gi khc) pht trin phng php ng ng thi, tin hnh nhng tnh ton u tin v l, ma theo phng php ng n v (cng trnh ca N.A.Vlicanp, M.I.Lvovich, E.V.Berg, G.A.Xanhin). Cng trong thi k ny M.A. Velicanp t nn mng cho vic phn tch cn nguyn qu trnh hnh thnh l ca cc sng ng bng, xut cc phng php iu kin v d

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bo dng chy cc sng trong ma h (X.U.Blinkp, K.P.Vaxerenxki, N.I.Gunevich) v d bo cc hin tng bng.

T nm 1938 Vin thu vn quc gia tr thnh Trung tm d bo thu vn. Vin tin hnh cng tc t chc nghnh d bo thu vn quy m ton quc. Nm 1941 ln u tin cc hng dn c th v phng php d bo thu vn v nhng quy nh v vic thnh lp v nh gi cc d bo c xut bn.

Vic nghin cu nhng phng php d bo mi trn c s nhng thnh tu t c trong vic nghin cu qu trnh hnh thnh l, quy lut chuyn ng ca nc trong sng v ngun cung cp nc cho sng trong ma h cng pht trin. Vn o to i ng cn b chuyn nghip v cng c cng tc d bo thu vn trong nhng nm ny cho php m rng nhanh chng hot ng tc nghip ca phng d bo thu vn trong cc i kh tng thu vn a phng. Cng tc tc nghip ca phng d bo thu vn thuc vin thu vn quc gia v cc d bo trung ng Matxcva cng pht trin nhanh chng. Ti nm 1940 tng s cc d bo v c bo thu vn hng ngy trong ton quc ln ti trn 40 nghn.

Trong nhng nm chin tranh i quc v i cng tc d bo thu vn chuyn hng cho ph hp vi tnh hnh thi chin. Vo nm 1945, t cc phng d bo thu vn ca Vin thi tit trung ng v Vin thu vn quc gia ngi ta thnh lp hai phng d bo ca vin d bo trung ng nay l trung tm nghin cu kh tng thu vn, trung tm ca c nc v phng php lun khoa hc ca cc dng d bo tby vn.

S pht trin nhanh chng ca ngnh thu li sau chin tranh t ra nhim v mi cho d bo thu vn. Vic xy dng cc kho nc ln i hi phi c cc d bo dng chy n trong tng thng tng qu, ma ng thi lm tng s lng d bo dng chy ngn hn.

-V nhng thnh tu khoa hc ca giai on ba c th k ti:

+ a ra thuyt gn ng v chuyn ng sng l, nghin cu c ch

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iu tit dng chy ca h thng sng ngi, ng lc hc ca lng tr nc trong sng v chy truyn ca nc theo dng sng.

+ Nghin cu qu trnh ngm trn lu vc.

+ Nghin cu cc hin tng tuyt trn lu vc v bng trong sng h.

+ M hnh ton cc qu trnh thu vn.

+ Nghin cu qui lut hnh thnh dng chy cc sng min ni.

Nhng thnh tu trn v nhng phng php d bo hon thin hn c tm ra trn c s c lin quan cht ch vi cng trnh nghin cu ca tp th cc nh thu vn thuc vin thu vn quc gia v vin nghin cu kh tng thu vn a phng (G.I.Ghisnic, I.A.Lixer, P.L.Netrex, A.A.Paxtos, G.I.Paxtukhovaia, V.N.Rukhatze, V.V.Xalazanop, I.N.Trenoivanhenco, A.A.Guxevaia, V.I.Bremivana...). Chnh h ngoi nhng lao ng tc nghip, son tho nhng phng php d bo c th cho tng sng ca nhng vng c c im a l khc nhau v do c cc c im khc nhau v ch thu vn.

1.2.2 .S lc lch s pht trin d bo thu vn Vit Nam.

Theo nhng ti liu trc ngy gii phng min Bc (1954) cn li th cng tc d bo thu vn hu nh khng c g. Ch c cc s liu quan trc m tuyt i a s l yu t mc nc ca cc trm t ti cc th x, nh Lai Chu, Ho Bnh (Sng ) Lo Cai, Yn Bi (Sng Thao), Tuyn Quang (Sng L), Thi Nguyn (Sng Cu). C vi cng thc tnh ton v d bo do mt k s ngi Php v mt k s ngi Vit a ra, nhng khng c vn bn no cho bit chng c dng trong d bo nh th no v kt qu ra sao. Vic theo di mc nc trn cc h thng sng bo v iu do Phng thu vn thuc nha cng chnh Bc Vit tin hnh.

Ch sau ngy gii phng, c s quan tm ca ng v Chnh ph cng tc d bo thu vn mi pht trin qua cc giai on sau:

cGiai on t nm 1955 n nm 1959.

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Cng tc thu vn ni chung c tin hnh ti hai c quan: Phng Thu vn thuc Nha kh tng v Phng thy vn thuc Cc Kho st thit k B Thu li kin trc. Trong thi gian ny, nhng ngi lm cng tc d bo thu vn xy dng c mt s phng php d bo n gin, ch yu l phng php d bo ti trm (xu th) v thi gian d kin t 0,5 n 1,5 ngy cho 4-5 trm trn h thng sng Hng nh H Ni, Ho Bnh (Sng ), Yn Bi (Sng Thao), Ph Ninh (Sng L). Ni dung phc v ch yu l theo di tnh hnh nc phc v bo v iu vng ng bng sng Hng.

dGiai on t nm 1960 n 1976

Cui nm 1959, Nh nc quyt nh thnh lp Cc Thu vn trn c s st nhp hai phng thu vn ni trn.

Phng d bo tnh ton thu vn v sau l phng d bo thu vn l mt trong cc phng chuyn mn ca Cc c chc nng theo di cnh bo, d bo thu vn cho cc h thng sng chnh min Bc phc v ch yu cng tc phng chng l lt, phc v sn xut nng nghip, giao thng vn ti v quc phng.

V lc lng trong thi gian u (1960-1963) mi c 1-2 k s tt nghip khoa Thu li trng i hc Bch khoa; i b phn l cc k thut vin c o to trong trng trung cp thu li v cc nhn vin kh tng thu vn c o to cp tc trong 6-7 thng. Nhng nm sau c thm mt s k s tt nghip thu vn nc ngoi.

V mng li trm in bo, trn c s quy hoch li trm c pht trin rt nhanh trong cc nm 1961 n 1963 li trm in bo cng c tng nhanh m bo theo di c cc hin tng ma l trn sng chnh, sng nhnh v sng con ton min Bc.

V t chc, c chuyn mn ho nhm m bo phn tch c chiu su v tch lu kinh nghim: Mt t nghin cu li trm in bo, quy nh m lut, ch in bo v t chc thu thp s liu p ng cc yu cu ca d bo thu vn. Mt t nghin cu quy lut hnh thnh l v tnh ton cc

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c trng thu vn t nn mng cho cc nghin cu qui m ln sau ny. Mt t d bo nghip v quanh nm, bin tp cc phng n d bo v tng kt nghip v, mi t c chia nh, d bo cho mi lu vc sng nhm tch lu kinh nghim phn tch d bo 3-5 nm li thay i v tr nhm o to cn b ton din.

Ti cc a phng, tt c cc Ty thu li thnh lp Phng Thu vn trong c 1-2 d bo vin chuyn trch, va m nhim in bo cho trung ng va bo cho a phng.

i tng phc v c m rng nhiu. T ch ch d bo ngn hn trong ma l c m rng sang d bo hn va, hn di phc v sn xut nng nghip, giao thng vn ti v quc phng.

u nhng nm 70 v c bn d bo thu vn c y cc hng mc d bo:

- D bo hn ngn (trc 1-2 ngy) cho cc h thng sng chnh min Bc. S v tr c d bo tng ln nhiu ln bao gm tt c cc trm cht trn cc sng, cc th x, cc v tr c hoc ang xy dng cng trnh.

- D bo hn va (5-10 ngy) d bo xu th mc nc v kh nng cao nht, thp nht trong tun.

- D bo hn di (1 thng, 1 ma) cc kh nng trung bnh, cao nht cho cc sng sui v cc cng trnh nc dng v vng nh hng thu triu.

V phng php d bo, c nhng bc tin rt ln.

- Trong nhng nm 1960-1964 ch yu dng phng php d bo ti trm, mc nc tng ng trm trn- trm di. Nh s v tr c phng n d bo c tng ln nhiu nn trn mt trin sng c th d bo chuyn v h lu tng thm thi gian d kin. Nh trm H Ni d bo c 48 gi v c bo thm 24 gi na. u im ca phng php ny l n gin, d ph cp v do x l ring cho tng on nn c th xt c th cc gia nhp khc nhau trn cc on sng khc nhau.

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Song song vi d bo tc nghip, y mnh cng tc nghin cu nghip v nhm gii quyt nhng kh khn ny sinh ra trong qu trnh d bo, ng thi t nn mng cho nghin cu cc phng n quy m ln, p dng k thut mi ca nc ngoi nh nghin cu qui lut truyn sng l trong sng cho hu ht cc on sng ca h thng sng Hng t bin gii v h lu. Thng qua c trng tc v thi gian truyn sng l, nghin cu qui lut hnh thnh dng chy do ma trn cc sng va v nh ton min Bc thng qua phng n tn tht v phng n chy tp trung lu vc (s dng cc loi ng n v), nghin cu lng tr nc trong sng cho h thng sng Hng vng trung h lu, nghin cu ng dng cc phng php din ton l ca nc ngoi vo cc sng Vit Nam.

- Nhng nm 1965-1971 l nhng nm m rng vic ng dng cc kt qu nghin cu vo nghip v hoc xy dng cc phng n ci tin. Ni bt nht trong nhng ng dng ny l phi hp phng php din ton l vi phng php ma dng chy x l nhp lu khu gia trong nhng on sng c nhp lu ln.

Trong vic d bo kh nht l d bo cho S pha T l mi ln v nh l. Nu l do ma thng ngun l chnh, dng chy s theo quy lut bnh thng nhng nc ta lng ma phn b rt khng u; nhiu trn ma bt u t h lu, gia nhp khu gia ln hn nhiu so vi dng chy t thng ngun v; thi gian truyn l cn rt ngn. Mc nc ti v tr d bo ln trc cc trm thng ngun, cng sut nc ln rt ln.

Nh cc kt qu nghin cu v thi gian truyn l v tch c gia nhp l gia, cho php xc nh c thi im bt u ln v cng sut l mi ln. Vic d bo cho S pha T l mi ln c bn c gii quyt.

Vn d bo nh l cng c nghin cu k. T vi ba phng n ri rc, cn c vo tng lu lng tnh c ca cc sng nhnh, chng ta xy dng c phng n d bo nh l t s liu ma trn c s tnh phn b ma theo khng gian v thi gian trn ton lu vc. Nh cch phn tch tng qut d bo sm c nh l v thi gian xut hin. Vn l

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khng u trn cc sng nhnh cng c nghin cu v ng dng sm. nh hng ca l khng u trn sng , sng Thao, sng L n l sng Hng hoc l khng u trn sng Cu, sng Thng, sng Lc Nam, sng ung n sng Thi Bnh c x l trong qu trnh d bo l c kt qu tt, k c trng hp t l l sng nhnh thay i trong qu trnh l.

Cc phng n d bo di hn trc mt thng, trc mt ma cng c xy dng. V ma cn c phng n d bo Moun dng chy trn cc sng sui vng ni v trung du; d bo nc n cc cng trnh; d bo dng chy trn sng ln v d bo chn nh triu cho cc trm vng nh hng triu. V ma l, c phng n d bo nh l cao nht cho cc trm khng ch cc sng ln min Bc, d bo dng chy trung bnh nm v phn phi lng nc n h cha. D nhin chnh xc d bo hn di cn cha th tho mn, do hn ch trnh khoa hc ni chung trong nc v trn th gii.

e. Giai on t nm 1977 n nay.

Sau ngy min Nam hon ton gii phng, nc nh thng nht, nghnh kh tng thu vn c thnh lp. B mn d bo thu vn cng c mt bc ngot quan trng c v t chc, phc v v tin b khoa hc k thut.

V mt t chc, Phng d bo thu vn st nhp vi phng Thng tin thnh Cc d bo kh tng thu vn. Lc lng d bo thu vn c tch ra thnh 3 b phn xy dng thnh cc phng d bo thu vn, ch o d bo a phng v nghin cu d bo kh tng thu vn. Ngoi ra cn mt s cn b i tng cng cho cng tc kh tng thu vn mt s tnh thnh pha Nam.

Nhim v phc v c m rng ra ton quc. Cn phi nhanh chng nm c c im thu vn a dng trn cc h thng sng thuc di t di v hp ca min Trung, ca cc h thng sng vng Ty Nguyn cng nh cc sng vng ng bng Nam B.

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Vic b tr trm in bo ma v thu vn c thc hin ngay trong cc nm 1977, 1978. n nay v c bn, li trm tng i n nh p ng c yu cu d bo phc v. S liu quan trc trn ton mng li trong ton quc trong ma ma l c th v cc d bo kh tng thu vn sau khi quan trc t 1-3 h.

Vic t chc d bo phc v 3 cp (Trung ng, i khu vc v i tnh) c hnh thnh; m bo nm bt c cc hin tng ma l sm v phc v ti ch c kp thi cho Trung ng v cho a phng.

Nhng nm gn y (c bit l t nm 1981) song song vi nhim v phc v chung nh trc, b mn kh tng thu vn phc v chuyn ngnh c hiu qu nh:

+ Phc v ngnh nng lng: phc v thi cng cng trnh thu in Ho Bnh, khai thc h cha Thc B, h n Dng.v.v.

+ Phc v giao thng vn ti: lp t khai thc v bo qun h thng cu phao qua sng, thi cng cu Thng Long, cu Chng Dng, iu hnh hot ng ca cng H Ni; phc v vn ti ng sng trn cc tuyn sng vng ng bng v vng trung du Bc B. . .

Hiu qu kinh t ca kh tng thu vn ang c nghin cu v nh gi.

V khoa hc k thut chng ta ang tch cc nghin cu v ng dng cc m hnh hin i vo tnh ton v d bo. Nh c my tnh in t nn kh nng ny ang tr thnh hin thc.

f. Phng hng pht trin b mn d bo thu vn trong nhng nm ti.

Trong tng lai, s pht trin ca b mn d bo thu vn ph thuc vo s pht trin ca cc nghnh khoa hc k thut c lin quan nh ton, l, c, my tnh, kh tng, hi vn, thng tin .v.v.

D kin trong nhng nm ti, b mn d bo thu vn s c pht

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trin ng b trn 3 ni dung sau:

1.1 Cng c v tng cng h thng c s trong d bo thu vn: mng li kh tng thu vn cng nh mng li in bo trn c nc s c pht trin hon chnh trn c s ti u nht v mt thu thp thng tin kh tng thu vn, ng thi kt hp s dng cc thng tin vin thm hin ti trn ton lnh th, cc loi v tinh kh tng thu thp cc thng tin phc v cho d bo ma trn nhng vng khc nhau, cc loi v tinh ti nguyn thu thp cc thng tin quan trng v lu vc nh lp ph, a hnh, lng sng, vng ngp, m .v.v. Cc loi thng tin rt cn thit cho vic m hnh ho, chun ho v nghip v ho cc m hnh ca d bo thu vn.

ng thi, cn xy dng mt h thng lu tr s liu hin i v hon chnh mt h thng thng tin hu hiu, lm vic trong mi tnh hung bt li nht ca thin nhin.

2.1 Cng c d bo v x l cc thng tin. Trong nhng nm ti cc loi my kch c ln nh EC1035 (trong chng trnh hp tc Vit X) loi c nh nh Roboton (trong chng trnh vin tr Quc t PNUD) loi my IBM.TI (trong chng trnh vin tr ca cc t chc Quc t) s c trin khai trong Tng cc, cng nh trong Cc d bo kh tng thu vn. Vic trang b cc loi thit b tnh ton hin i s lm thay i mt cch ng k i vi cng tc d bo thu vn trong nhng nm ti. N s to iu kin cho vic hon thin cc phng php hin c, ng thi ng dng mt cch nhanh chng cc m hnh s tr hin i nh kiu m hnh SSARR, TANK, SACRAM-ENTO, SOGREAH, SAINT VENANT,.v.v. Phn u trong nhng nm ti xy dng c mt h thng m hnh hon chnh m t c ton b tc ng t dng sui t thng ngun ra ti ca sng cho h thng cc sng ln v va nh h thng sng Hng-Thi Bnh, sng Cu Long, sng M, sng C, sng Thu Bn, sng Rng, sng ng Nai v.v. H thng cc m hnh phi mm do, thao tc nhanh chng v c kh nng lm vic trong mi tnh hung c th xy ra do tc ng ca thin nhin cng nh con ngi, nh c tc ng chm l ca h cha v vng trng, c lm vic ca cng trnh phn l, c v vi bt c on no trn h thng sng, c th c v

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nhng p chn nc, ng thi li c l ni ng v c nc dng ca bin.

Ngoi ra v phng din d bo hn va, hn di trong thu vn cn phi xy dng mt h thng lu tr p ng c yu cu ng thi pht trin cc loi phng php: phng php phn tch chui thi gian chng hn nh m hnh ARIMMA, cc phng php vt l thng k xt tng quan cc yu t thuc loi m hnh tt nh kt hp vi d bo ma di hn.

c. V cng tc phc v v hiu qu ca n. Mc tiu cui cng ca cng tc d bo l lm cho bn tin pht ra phi a li hiu qu cao nht.

iu c ngha l bn tin phi cha nhiu thng tin c ch, r rng nht, chnh xc cao, thi gian d kin c sc thuyt phc, truyn tin nhanh nht v ng i tng nht. Cui cng cc i tng s dng bn tin d bo phi hiu c bn tin v phi c tc ng ngay khng tr hon.

V vy, trong nhng nm ti vic phc v d bo thu vn s tp trung vo cc vng nng nghip trng im ca Nh nc nh ng bng sng Hng v sng Cu Long. ng thi m rng din phc v ti a bn huyn v hng vo phc v su cc chuyn ngnh.

T nay n nm 2000, vi mc tiu trng im l tip thu v khai thc c hiu qu cc cng ngh tin tin thc hin hin i ho ngnh vi tc nhanh hn, cng tc d bo thu vn s c nhiu bc tin mi mnh m hn v t chc, nhn lc, cng ngh, b mn, i tng phc v,... vi nhng phn u mi: d bo sm hn mt gi, di ngy hn, chnh xc hn nhm p ng ngy cng tt hn mi yu cu ca cc nghnh kinh t quc dn, c bit ca cng tc phng trnh l lt v qun l khai thc ngun nc, mang li cho x hi nhiu li ch v gi.

1.3. Vai tr ca d bo thy vn trong khai thc v qun l ngun nc.

Trong thc t, lng nc phn phi theo khng gian thi gian khng u, ni nhiu nc gp 15- 20 ln ni t nc, ma l chim 70- 80%, cn ma cn ko di ch chim 20- 30% tng lng nc trong nm m nhu cu

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dng nc trong ma kh hn thng rt nhiu. Cng vi s pht trin ca x hi, yu cu dng nc ngy cng tng m cc trng thi t nhin ca dng chy sng ngi khng p ng c cc yu cu ny. V vy, nc ta v ang xy dng rt nhiu cng trnh: 75 h thng thu li ln, 650 h cha ln v va, 3500 h cha lai nh, 1000 cng ly nc, 2000 trm bm, khng ch, iu tit dng chy t nhin p ng cc nhu cu v ti, tiu, pht in, vn hnh, bo v cng trnh, tr nc trong ma l v iu tit, cp nc, sn xut in trong ma cn. Hn 20 nm qua, mt b mn thu vn mi hnh thnh v pht trin: d bo phc v thi cng, qun l, khai thc cng trnh, iu tit, ct l... Vi nhng bn tin ring, chuyn su phc v thng xuyn cng tc khai thc v qun l cc cng trnh trn, d bo thu vn t c nhng kt qu phc v sau:

1.3.1. Phc v thi cng v khai thc cng trnh thu in vi mc tiu an ton, vn hnh ti u, hiu ch kinh t cao.

- Phc v thi cng, khai thc v iu hnh cng trnh thu in Ho Bnh: Trong giai on thi cng 1982- 1986, tin hnh d bo tnh hnh mc nc trc 1- 2 ngy, 5- 10 ngy, 1 thng, 1 ma. c bit trong hai t ngn sng : 1982- 1983 v 1985- 1986, d bo thu vn d bo c nhiu trn l t xut, tri ma, gp phn tng tc thi cng, tit kim hng ngn ngy cng, trnh c nhiu thit hi, mt mt, m bo thi cng an ton, ch ng, phng chng l thng li.

- T 1986 n nay tin hnh d bo vi cht lng ngy mt tng: dng chy n h trc 1- 2 ngy, 5- 10 ngy, 1 thng, 1 ma v d bo phn phi dng chy nm nhm phc v ct l, tch nc, x nc n l u ma, iu tit, pht in, chng l an ton cho cng trnh v h lu.

- Phc v vic thi cng v khai thc nh my thu in Thc B- cng trnh ln u tin min Bc: t nm 1980 n nay, d bo lu lng n h trc 1- 2 ngy, 5- 10 ngy, 1 ma.

- Phc v cng trnh thu in Ialy- cng trnh trng im: t 1993 n nay, d bo thu vn tin hnh nhn nh dng chy v phn phi trong nm,

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cc c trng dng chy n tuyn cng trnh hng ngy, 5 ngy, 10 ngy v hng thng nhm gip ban qun l lp k hoch cng tc, m bo cng tc ng tin , bo v cu thi cng v vt t my mc ti tuyn cng trnh. Ngoi ra, phc v vic ngn sng Ssan thng li, d bo thu vn cp cc bn tin nhanh, chnh xc, kp thi v thi k kh kit nht tho mn cc iu kin cho php ln, lp sng; v tc dng chy trn knh dn nc ti tuyn lp sng; v chnh lch u nc thng h lu cng trnh khi co hp dng trong cc thi k lp sng t 1, t 2 ...

D bo thu vn cn ng vai tr quan trng v mang li nhiu li ch ng k trong vic phc v qun l ngun nc v vn hnh nhiu h cha khc nh Tr An, Du Ting, a Nhim, Sng Hinh . . .

1.3.2- Phc v ti tiu: p ng cc yu cu ti nc phng hn, tiu nc chng ng, tham gia iu tit cc h cha v m bo an ton cho cc cng trnh thu li trn ton quc.

- Ngoi nhng d bo thng k, t nm 1985 n nay, tin hnh d bo mc nc trc 24h, 36h, 48h v trc 1 ma ca mt s trm trn ton quc, cp cho cc qun l nc phc v ch o sn xut, ch o cc h thng thu nng vn hnh ti 5,4 triu ha, tiu 1,9 triu ha, phng hn, chng ng.

- Cng hn 10 nm nay, d bo thu vn cp tin d bo mc nc ti p Cu (sng Cu), Thng Ct ( sng ung) trc 24h, 36h, 48h khi mc nc p Cu ln hn bo ng II trong ma l v mc nc cao nht, thp nht ngy trong ma cn phc v x nghip thu nng Bc ung c k hoch bm tiu, chng l lt c hiu qu v gip cho dn c ca c mt vng rng ln khng b ngp lt.

1,3,3, D bo thu vn phc v giao thng ng thu

Nc ta c h thng sng dy c ni cc a phng, thng sut t bin ln cc vng trung du v c min ni, rt tin cho giao thng ng thu. Mt trong cc nhn t nh hng ti hiu qu ca khai thc h thng giao

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thng ng thu l cc thng tin d bo thu vn hn va v hn di.

Ma cn t d bo mc nc ti cc im chnh, tin hnh d bo su cho tng lung, sau ln biu an ton cho cc loi tu v lp k hoch vn ti. Ma l khi nc trn ln cc bi, xo i ranh gii gia lng chnh v bi, khu ng an ton khi qua cc cu cng gim, tc nc trn cc on sng ln l nhng cn tr cho cc phng tin gia thng ng sng. V vy hot ng ca ngnh giao thng ng thu lc no cng gn lin vi d bo thu vn.

1.3.4. D bo thy vn phc v cc h thng thu nng.

Cc h thng thu nng l b my iu ho lu lng nc cho mt vng nng nghip. Khi thiu n cn b sung nc ti, khi tha n cn tiu nc ra khi h thng thu nng. lm c iu ny vi mt chi ph nh nht th khng th khng c s tham kho cc thng tin v d bo thu vn. Ngoi ra d bo thu vn cn cung cp nhng thng tin v din bin mn cho cc cng trnh bm nc t sng vo ti cho ng rung ng yu cu sinh thi ca cc loi cy trng.

1.4. D bo thu vn phc v chng thin tai, l lt

Lch s ghi li nhiu trn l lt gy thit hi to ln v ngi v ca trn nhiu h thng sng trn th gii. Ti Vit Nam, trn h thng sng Hng-Thi Bnh trong nhng thp k gn y c 2 trn l (1945, 1971) gy v hng lot v km theo thit hi v nhiu mt. L nm 1945 gp phn vo nn i nm lm cht 2 triu dn. Trn h thng sng Cu Long trn l nm 1961,1978, 1984, 1994, 1996 v mi y nm 1997 l nhng trn l ln gy nhiu thit hi c bit l nm 1997 gy thit hi trn 5000 t ng v hng trm ngi cht. Nu d bo c cc hin tng ny trc thi gian di, c cc bin php phng trnh s gim c thit hi do n gy ra.

Nhng bin php thu li chnh phng chng l l , phn l, ct l v chm l. Song mun qun l khai thc tt cc h thng trn cho nhim v

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phng chng l cn phi c nhng thng tin v din bin cc qu trnh mc nc v lu lng trn cc h thng sng.

Hng nm cc d bo tin hnh hng lot cc d bo phc v phng chng l cho trung ng v cc a phng nh d bo mc nc cho cc trm thu vn trng yu trn h thng cc sng chnh v cc im ch cht (H Ni- Trn sng Hng, Ph Li- trn sng Thi Bnh, Nam n- trn sng C, Ging- trn sng M, Tn Chu- trn sng Tin, Chu c- trn sng Hu).

Te nay n nm 200, vi c mc tiu trng im l tip thu v khai thc c hiu qu cc cng ngh tin tin thc hbin vic hin i ho ngnh vi tc nhanh hn, cng tc d bo thu vn s c nhng bc tin mi mnh m hn v t chc, nhn lc, cng ngh, b mn, i tng phc v, vi nhng phn u mi: d bo sm hn mt gi, ngy di hn, chnh xc hn nhm p m p ng ngy mt tt hn mi yu cu ca cc ngnh kinh t quc dn, c bit ca cng tc phng trnh l lt v qun l khai thc ngun nc, mang li cho x hi nhiu li ch v gi.

1.5. Phn loi d bo thu vn

1.5.1- Phn loi d bo thu vn theo hin tng

1. D bo ch thu vn

- Qu trnh mc nc (H), lu lng (Q) ..

2. D bo cc c trng thu vn H,Q ln nht, trung bnh, nh nht v thi gian xut hin.

3. D bo tng lng dng chy.

4. - D bo xm nhp mn

5. Cc hin tng bng trn h.

1.5.2- Phn loi theo quy lut chuyn ng nc

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1. D bo da trn quy lut chuyn ng nc trong sng min ni.

2.D bo da trn quy lut chuyn ng nc trong sng v trn lu vc ng bng.

3.D bo da trn quy lut chuyn ng nc trong sng, trn lu vc v cc hon lu kh quyn, tc ng ca yu t khc phc tp nh bo, triu cng .v.v.

1.5.3- Phn loi theo thi gian d kin

Da trn i hi ca sn xut v thi gian chy truyn nc trn sng v trn lu vc.

- cc nc, trn cc sng ln, di th d bo thu vn hn ngn c th c thi gian d kin nh hn 2 ngy, hn va - t 2- 10 ngy, hn di t 10 ngy n 1 nm.

- nc ta cch phn loi theo quy phm d bo 94 TCN7- 91 ( Xem bng 1.1) Bng 1.1 Phn loi d bo theo thi gian d kin Vit Nam.

Ngn Va DI Siu di

< 10 ngy 10 ngy- 1 nm hn 1 nm

l thi gian tp trung nc trung bnh trn lu vc.

1.6. Mt vi khi nim quan trng

1.6.1 Phng php v phng n:

- Phng php l cch tin hnh gii bi ton d bo, da trn mc tiu d bo v cc thng tin d bo.

V d 1: Phng php biu hp trc

V d 2: Phng php phn tch chui thi gian

V d 3: Phng php hi quy tng bc

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- Phng n d bo l cc biu , phng trnh, h phng trnh v cc bt phng trnh c th m phng cc iu kin rng buc c th cho trm sng no . Di y l cc v d v cc phng n d bo:

V d 1: Biu quan h mc nc tng ng gia trm H Ni v Tng lu lng cc trm Ho Bnh, Yn Bi v V Quang.

V d 2: Phng trnh quan h mc nc ti H Ni vi lu lng cc trm tuyn trn.

V d 3: Cng ngh d bo mn: SALFOR

1.6.2- Cc bc tin hnh xy phng n d bo

Mun d bo mt yu t Y l hm tng quan vi cc nhn t X1, X2,, Xm, ta cn tin hnh cc bc sau:

8.1 Nghin cu, phn tch quy lut hnh thnh yu t cn d bo Y, t xc nh c cc nhn t nh hng. Trong mc ny i hi nhiu ti cc kin thc chuyn mn v kinh nghim d bo. Chn ng, chn tp nhn t nh hng l nh hng v cng quan trng v m bo vng chc cho thnh cng trong vic xy dng phng n. Trong trng hp cc l gii v ngha vt l cn kh khn, cha r rng, c th dng cc thut ton thun tu thng k, nh gi mc tng quan v kh nng d bo yu Y khi bit cc nhn t nh hng X (x1,x2,x3,.....). Vn ny s c cp trong cc phn sau.

8.2 Nghin cu iu kin thng tin cho php (s liu dng nghin cu phi ph hp vi kh nng p ng trong phng n d bo nghip v) v chn m hnh d bo.

- Xut pht t cc quy lut hnh thnh yu t Y, xc nh vct nhn t d bo. Trong iu kin hin nay nhiu nhn t cha c cc quan trc hoc c quan trc song khng c in bo. Nhng nhn t ny s khng c ngha trong phng n d bo.

- M hnh d bo c chn da trn kh nng quy m d bo v iu kin p ng thng tin d bo cho n.

26

Trong d bo kh tng thu vn hn va v di hin nay hu nh ch s dng cc m hnh thng k m khng dng cc m hnh tt nh. iu ny c gii thch bng cc l do sau:

a- Cc m hnh tt nh i hi y v chi tit cc thng tin d bo m trong iu kin hin nay cha p ng c.

Tnh a dng v s bin i phc tp trong khong thi gian d kin di hng tun, thng, ma cng ang nm ngoi kh nng m phng cc m hnh tt nh.

1.7. nh gi chnh xc v bo m d bo thu vn

nh gi sai s d bo ngi ta dng phng php ton thng k. Xc nh l, sai s ca tng tr s d bo l ngu nhin v phn phi ca n ph thuc vo phn b chun.

( )P x =

12 2

2

2 exp (1.1)

P(x) sai s chnh lch bin ngu nhin x vi chun ca n x ,

- gi tr chnh lch : lch tiu chun trung bnh ca x (phng sai)

1 - Sai s d bo: (denta)

= y - y (1.2) Chnh lch ca mc nc (hoc lu lng) thc o y v mc nc DB, y.

2 - Tnh sai s cho php d bo l - sai s cho php ca d bo l hn ngn bng 1 trong nhng lch xc sut sau y: ( - xicma)

cfS = 0 674, (1.3)

3 - Phng sai ca yu t d bo theo quy phm 94- TCN- 91 c tnh theo

27

cng thc sau:

( ) =

in

y yn m

2

1 hoc ( )

=

in

y yn

2

1

1 (1.4)

yi - gi tr yu t,

y - gi tr trung bnh.

n - s yu t dy.

m - s bc t do trong quan h dng d bo.

4 - Trng hp thay i tr s theo thi gian d bo, th sau s cho php d bo tnh nh sau:

Scf = + 0.674 (1.5) Trong - Phng sai chnh lch thi gian d kin

( )

= in

n

2

1

1 (1.6)

I - thay i bin ph thuc theo thi gian d kin, - gi tr trung bnh ca bin .

1.8 nh gi phng n d bo

nh gi phng n hoc m hnh d bo, dng t s tng quan (eta)

=

1

2S (1.7)

( )

Sy

n

yn

= ' 2

1 (1.8)

28

Nh vy nu bit t s S/, rt d dng tm c t s tng quan Phn loi d bo theo tiu chun cht lng nh sau:

Bng 1.2

Cht lng P/a d bo S/ Mc bo m ca P/a d bo

Tt

t

Dng tm

Khng dng c

75

> 60

< 60

Bi tp: Xc nh sai s cho php ca phng n mc nc vi thi gian d kin 5 ngy.

== = = =

10

51050100

23

0 674 23 16

cm

cm

cmcf

, .

Theo cng thc (6.1)

cfS cm= = 91810561

13

Ch tiu S = =1323

0 56,

Theo cng thc (6.1) phi c mt bng nc tnh S (tnh trung bnh sai s d bo 5 ngy).

Bng 1.3 Tnh ton sai s d bo. S TT

Thi gian t

Mc nc (cm) H= Ht-Ht+5 H -H ( ) H H 2 Ht Ht+5 1 2 3 4 5 6 7 1995

29

S TT

Thi gian t

Mc nc (cm) H= Ht-Ht+5 H -H ( ) H H 2 Ht Ht+5 1 2 3 4 5 6 7 1 2 3 4 5 6 7 94 95 96 97 98 99 100

1/VI 2/VI 3/VI 4/VI 5/VI 6/VI 7/VI 1956 25/VIII 26/VIII 27/VIII 28/VIII 29/VIII 30/VIII 31/VIII

205 203 199 195 192 188 184 98 102 103 105 108 108 108

188 184 180 176 173 160 166 108 108 110 110 111 111 112

17 19 19 19 19 19 18 -10 -6 -7 -5 -3 -3 -4

7 9 9 9 9 9 8 -20 -16 -17 -15 -13 -13 -14

49 81 81 81 81 81 94 400 256 289 225 169 169 196

997 51050 TB 10 cm

Bng 1.4 Tnh ton sai s d bo. S TT Thi gian Mc nc

Sai s d bo = Ht -Ht

2 Thc o

(Ht) D bo (Ht)

1 2 3 559 560 561

1945 1/VI 2/VI 3/VI 1956 29 30 31

205 203 199 108 108 108

200 198 195 115 118 123

5 5 4 -7 -10 -15

25 25 16 49 100 225

91840

Nh vy: S = 0,8 D bo c chnh xc cao .

S = 0,6 chnh xc c tng.

S = 0,4 c m bo 90%.

30

0,4 < S = 0,6 c m bo 90% n 75%.

0,6 = S < 0,8 chnh xc 75% n 60%.

v S > 0,8 chnh xc nh hn 60%.

31

Chng 2. H PHNG TRNH DNG KHNG N NH SAINT VENANT

2.1. Cc dng chuyn ng ca cht lng trong knh h Khc vi dng chy trong ng, c mc nc t do, chu tc dng ca p lc khng kh, tnh ton dng chy kh khn phc tp, mc nc thay i theo thi gian khng gian, h, Q, i, y knh... c quan h vi nhau v c th phn ra bi ton 1, 2, 3 chiu - nhng thc t bi ton thu lc ch hn ch 1 chiu vi Q v h. Da theo s thay i su dng chy theo thi gian v khng gian phn dng chy thnh: n nh v khng n nh.

2.1.1. Dng n nh Dng n nh l dng c su h, c tc V v mt ct khng thay i theo thi gian. Dng n nh c dng u v dng khng u. Dng u l dng c cc c trng thu lc nh mt ct, tc khng i theo ng i. Dng u: theo chiu di dng chy l dng c tc , din tch mt ct khng thay i theo chiu di, c ngha l V = const, = const theo s. Dng khng u l dng c cc c trng thu lc thay i theo S. Dng khng u: V = f1 (S), = f2 (S). Dng khng n nh l dng c v, thay i theo khng gian v thi gian. Dng khng n nh: V = f1 (S, t) = f2 (S, t). Dng khng u: c dng thay i chm v dng thay i gp. Chuyn ng ca sng l trong sng l chuyn ng khng n nh, l dng khng u thay i chm. Chuyn ng ca nc x t thng lu cng trnh trn v h lu nh nh my thu in Ho Bnh l dng khng u thay i gp.

32

2.1.2. Chuyn ng khng n nh -Dng khng n nh l dng c v, thay i theo khng gian v thi gian. -Dng khng n nh: V = f1 (S, t) = f2 (S, t). -Dng khng u: c dng thay i chm v dng thay i gp. 1. Cc loi chuyn ng khng n nh trong knh h : Trong trng hp dng khng n nh, mc nc c dng sng. Sng nc chuyn ng l sng di, c cong nh, di sng gp 100 - 10.000 ln cao ca sng. Khc sng gi trong h, bin, sng trong knh h vn chuyn c lu lng nc ln (sng chuyn). C nhiu loi sng trong knh h: - Sng thun: truyn theo dng chy. - Sng nghch: ngc chiu dng chy. 2. Cc c im sng x, sng l, sng triu trong sng. - Sng x: tng gim lu lng, c mc nc nhiu ng. - Sng l: khng c mc nc nhiu ng l sng thay i chm. - Sng triu: ln xung c chu k, mc nc l mc nc nhiu ng. 3.Quan h lu lng - mc nc trong dng khng n nh Dng n nh, quan h Q = f (Z) ln nht Dng khng n nh; khi nc ln: Q - Z c dng vng dy c th c mt hoc nhiu vng dy. i vi sng vng triu: quan h Q - Z c dng xon c.

2.2. Phng trnh vi phn c bn ca dng khng n nh thay i chm

2.2.1. Phng trnh lin tc Phng trnh lin tc th hin mi quan h gia cc yu t thu lc lin tc trong mi trng cht lng thng p dng cho bi ton 1 chiu c ngha l i vi 1 mc nc c cc c trng, cc thng s sau: lu lng, tc trung bnh mt ct, bn knh thu lc v .v.v...l hm 1 bin theo dc sng L. Trong giai on l, phng trnh lin tc c 2 bin l L v t. Gi thit, Q: lu lng, : din tch mc nc, dl cho 1 on sng, dt - thi gian. Xem mt on sng c Qdt ( lng vo) v

33

Q Ql

dl dt+

: lu lng xut lu.

R rng

+ dllQQ l lu lng mc nc ca ra.

Do , tng lng nc trong on sng bin i

Qdt - dtdllQQ

+

= - Ql

dldt ( . )21

Nu c dng chy gia nhp q cho 1 thi gian trn 1 chiu di sng l q dldt, khi bin i tng lng trong on sng vi thi gian dt s l

q dldt - )2.2(dldtlQ

N lm thay i mc nc vi tr s dllQ , trn 1 on sng c dng hnh ch

nht

lQdldt

t

= Ly (2.2) bng (2.3) v n gin dl dt ta c

tQl

q+ = ( . )2 4 Nu khng c lng gia nhp ta c:

)5.2(0=+lQ

t

y l phng trnh Saint Venant th 1 v l phng trnh lin tc ca dng chy. * Nu thay Q = V . th (2.5) c dng:

( )Vl

B Ht

+ = 0 Hoc

Vl

Vl

B Ht

+ + = 0

2.2.2. Phng trnh cn bng ng lc ca dng khng n nh Phng trnh chuyn ng ca sng l (a ra bi Bussinet) cho rng tng tt c cc lc trn 1 n v khi lng l bng 0 C th l: -gI + u + F = 0 (2.6)

34

Trong : g -gia tc trng trng I - dc mc nc u - lc qun tnh F - lc ma st dc c th chia thnh 2 thnh phn: dc i trong chuyn ng n nh v

dc ph gia dhdl

xut hin khi chuyn ng l, nh vy:

I = i - dhdl

(2.7)

h - su dng chy i vi dng sng c tc ln c th cng nhn nh lut bnh phng theo cng thc chezy V C RI= (2.8) V - tc trung bnh trong mt ct, R - bn knh thy lc, C - h s chezy Khi lc ma st bng tch trng lc n v nc trn dc vi 1 n v khi lng nhn c:

F gVC R

=2

2 (2.9)

Lc qun tnh, theo phng trnh Bussinet c th c trng bi 2 thnh phn:

U =

vt

V V+ l (2.10) Lc ban u, khc phc ma st trong mt ct, lc th 2 khc phc s bin i tc theo chiu di dng chy. Nh vy, tnh n lc qun tnh phng trnh ng lc c dng

i dhdl

VC K g

Vt

Vg

Vt

= + +2

2

1 2 11 ( . )

Phng trnh (2.11) l phng trnh th 2 ca Saint- Venant c th dng tnh ton chuyn ng sng l cho cc vng khc nhau. * Lc dng chy theo 2 chiu (chy ngc, chy xui) nh cc sng chu nh hng thy triu th phng trnh ng lc c dng

i dhdl

V VC K g

Vt l

Vg

= + +221

22 12

( . )

Phng trnh (2.12) l phng trnh 2 ca Saint Venant xut 1871. Tt nhin, c 4 thnh phn l c bn: (1) dc mc nc, (2) dc ma st

35

(3) dc qun tnh (4) dc i lu; trong mt s trng hp c th cn thm: lc do xoy (Se), lc do gi (Wf). dc tn tht xoy c xc nh bi 2.13

Se Keg

Q Ax

=2

2 132

( / ) ( . )

Trong : Ke - h s phn tn hay tp trung, du - l phn tn (khi (Q/A)2/x l m) v ngc li l tp trung. dc do gi: sinh ra chng li lc cn ca gi trn mt nc c xc nh bi 2.14. Fw = w Bdx (2.14) w - ng sut ct ca gi, c th vit i th nh sau: w = pCf VrVr

2215( . )

Trong Vr tc cht lng, k hiu |Vr|Vr s dng khi w vi chiu ngc phng ca Vr v Cf l h s ca ng xut ct, tc trung bnh ca nc l Q/A hp vi phng tc gi l Vw vi phng ca gc , nh vy tc ca nc quan h vi khng kh l

Vr QA

Vw= cos ( . ) 216 V lc gi:

Fw = = pVCf VrVrBdx WfBpdx2

(2.17)

Trong yu t lc ct ca gi l Wf Wf = Cf VrVr / ( . )2 218

Ghi ch chiu ca gi l ngc vi chiu ca dng chy.

2.2.3. Phn loi m hnh din ton phn phi Theo ngha vt l phng trnh moment c phn thnh: - Loi thnh phn gia tng cho a phng; n din t bin i moment bng bin i tc theo thi gian. - Loi thnh phn gia tng i lu, n din t bin i tc dc sng. - Loi thnh phn lc p, n tng quan vi chiu su theo knh. - Loi thnh phn trng lc, n tng quan vi dc sc cn Sf.

36

Trng hp h phng trnh Saint venant (b qua q, Fw, Fe, = 1) th vit theo phng trnh lin tc:

- Dng bo ton:

Qx

At

+ = 0 219( . ) - Dng khng bo ton

V

yl

yvx

yt

+ + = 0 2 20( . ) - Dng khng bo ton (vi n v chiu rng)

Vt

V Vx

g yx

g So Sf+ + =( ) ( . )0 2 22 ------------ Sng ng lc. ------------------ Sng khuch tn (p/tr trng thi tc thi). -------------------------- Sng ng lng. Thnh phn gia tng a phng, gia tng dng thng mang hiu ng qun tnh dng chy. Trng hp c hiu ng mc b, khng nh hng ti cc phng php din ton. Phng php tch phn chp khng th thc hin c trong tnh ton dng chy khi c hiu ng nc b v khng c c hc, thy lc din t s nh hng bin i dng chy trong sng theo moment. M hnh din ton phn phi n gin nht l m hnh sng ng lc, b qua cc gia tng g(So - Sf), gi s So = Sf ( dc thy lc v dc ma st cn bng vi nhau). M hnh sng khuch tn: hp nht thm vi gi tr p sut (b qua gia

tng g y )

M hnh sng ng lng: gi li tt c gi tr gia tng tc v p sut trong phng trnh moment. Phng trnh moment c th vit di dng tnh ton, th d nh dng chy n nh hoc khng n nh v ng dng hoc a dng. Trong phng trnh

lin tc At= 0 cho dng n nh v gia nhp khu gia q = 0 cho cc dng sau:

Dng bo ton: 1 1 2 23

2

gAQt gA

Q Ax

yu

So Sf

+ =

( / ) ( . )

37

Dng khng bo ton:

+ =1 2 24g

Vt

Vg

Vx

yx

So f

( . )

------n nh dng chy ng dng ------------n nh v dng chy a dng ----------------------khng n nh, dng chy a dng

2.2.4. Nm gi thit ca phng trnh 1. Xem nh chuyn ng cht lng 1 chiu. Vi ngha l coi nh chuyn ng nm ngang v thng ng l khng ng k so vi dc sng. Do dc dng chy l ging nhau trong cc mt ct. Gi thit nh vy c ngha l khng c dc nm ngang. 2. Chuyn ng theo gi thuyt l thay i chm, vi ngha khng c tn tht dc a phng. 3. Gi thit l sng di, nh vy su mt nc rt nh so vi chiu di ca sng, mt vi tc gi gi l l thuyt nc nng. iu dn ti phn phi nh lut p lc thu tnh theo chiu su, c ngha l b bt p lc d do gia tc nc theo chiu thng ng. 4. Lc cn trong phng trnh c dng nh chuyn ng n nh.

1. dc y sng l rt nh.

2.3 Xp x ca sai phn (Sai phn ha)

2.3.1. Khi nim chung Phng trnh Saint Venant cho din ton khng c phng php gii

tch phn (tr 1 vi trng hp c bit). N l phng trnh vi phn tng phn (o hm ring) ni chung c th gii bng phng php s tr v phng php c trng.

Trong cc phng php trc tip (s tr) xy dng t phng trnh sai phn ban u t phng trnh lin tc v phng trnh moment.

Li gii cho cc c trng dng chy c nhn t bc khng gian l v bc thi gian t.

Trong phng php c trng, phng trnh o hm ring u tin chuyn sang dng c trng, v sau phng trnh c trng c gii theo

38

phng php phn tch, nh trong vic gii sng ng hc, hoc s dng phng trnh o hm ring.

Trong phng php s gii bi ton o hm ring, vic gii a sang vic gii bng li X - t. Li X - t c xc nh bi bc khong cch x v bc thi gian t. Nh trong hnh 2.1, nhng im li c ch theo k hiu i (theo khong cch), theo thi gian l j. ng theo thi gian l vung gc vi x.

S s tr chuyn phng trnh o hm ring ti hng lot phng trnh vi phn i s hu hn. Phng trnh vi phn hu hn trnh by sai phn ring v tm thi trong cc im cha bit trn ng thi gian tng lai j +1, v ng thi gian hin ti j. Trong tt c gi tr khng bit c tnh t tnh ton bc ban u (xem hnh 2.1).

Hnh 2.1 S li sai phn.

Li gii ca Saint Venant bit trc t thi gian ny n thi gian sau c tnh mt cch lin tc.

2.3.2- Phng php sai phn C th sai phn ha trc tip h phng trnh c bn gii m khng

cn chuyn qua phng trnh c trng. Tt nhin, cch gii nh th i hi mt khi lng tnh ton rt ln nhng nh c my tnh in t nn vic gii quyt rt thun tin. Nh cch ny c th tnh c cc trng hp rt phc tp, sng c bi, sng c mt ct thay i, li sng phc tp .v.v. m cc phng php khc hu nh khng th gii quyt c. Trong nhng nm gn y, ngi ta thng dng phng php sai phn gii cc bi ton dng

xxxx

t

2 1

0 1 2 3 4 s

S02 S01

t

39

khng n nh trong thc tin v ni chung l gii bng my tnh in t.c im chung ca phng php sai phn l chia knh ra thnh nhng on ngn S v chia thi gian thnh nhng thi gian nh t. Nh vy, trong ta (s-t) c chia thnh cc li, trn ta s xc nh c cc yu t ca chng ti cc nt ca li, tc l ti cc mt ct nh trc v vo cc thi im nh trc (xem Hnh 2.1).

Trn mi li nh th, cc o hm ring trong h phng trnh c bn s c thay bng t s cc gia s.Sai phn c th nhn c t hm U(x).Trong Hnh 2.2, phng trnh Taylor ca U(x) t x+x.

U(x+x)= U(x) + x U (x) + 12x 2 .U(x)+ 16 x

3.U(x)+...

U' (x) = 4/x, U"(x) = 2U/x2 ... Lit Taylor t x = x l U (x - x) = U (x) - x U'(x) + 1

216

2 3 x U x x U x t"( ) "( )

Sai phn trng tm tng t dng (2.2) tr (2.1) U (x + x) - U (x - x)= 2x U' (x) + 0 (x3) Trong : 0 (x3) l d tha ca bc 3 v bc ln hn Gi thit U' (x), gi s 0(x3) = 0, cn li U' (x) = U x x U x x

x( ) ( )

(+ + 2 0 x

3)

N c sai s tng t bc x2, y l sai s, do dng bc cao, nh sai s ct ct. Sai s tin tng t nh xc nh tr U(x) t (2.1)

U (x + x) - (U(x) = x U'(x) + 0 (x2) Hnh 2.2

u u(x+x)

u(x)

u(x-x) i-1

i+1

x-x x x+x

x

40

Gi thit bc hai v cao hn l khng ng k - Ta c:

U' (x) = U x x U xx

o( ) ( )

(+ + x

2)

Vi sai s tng t nh bc ca x Sai s li, tng t nh dng nh sai s t (2.2) tr U(x) U(x) - U(x - x) = U(x) . U'(x) + 0(x2) Gii cho U'(x) c

U'(x) = U x U x xx

x( ) ( ) ( ) + 02

C nhiu s sai phn c th chia thnh hai loi s : S sai phn hin v s sai phn n s khc nhau gia chng l:

s hin l gii n trong mt qu trnh di mt li hoc hai li gn nhau tnh cc y t thu lc trong tng nt.

S sai phn hin c iu kin l khng s dng x, t nh cho bi ton hi t.

S sai phn n : vi x, t ln khng i hi iu kin. S hin

S sai phn hin l s m sau khi sai phn ho h phng trnh (2.1) (2.2) ta c h hai phng trnh i s vi hai n s Q, mt nt cha bit v do c th gii ngay ra cc n s . V d s hnh thoi (2.3). S ny i hi khong cch gia cc mt ct s phi bng nhau, thi on tnh ton t phi c nh. Thay o hm ring bng cc biu thc sai phn sau y:

t

B At

=

2

s

D Cs

= 2

Qt t

B AQ Q=

2

Qs s

sD CQ Q=

2 Nu c trng ti hai lp thi gian trc (nt A, C, D) bit th khi

41

sai phn ho h phng trnh Saint venant ta c hai phng trnh n s bc nht vi hai n s l QB, B ti nt B lp thi gian sau. Gii h ny ta tm ra ngay c cc c trng QB, B.

Nh vy bng s sai phn ny ta c th tm c cc c trng cha bit lp thi gian sau khi c trng ca hai lp thi gian trc bit. Bng vic cho trc cc c trng Q, ca hai lp thi gian ban u (iu kin ban u) ta tm cc c trng cha bit ln lt lp thi gian ny ti lp thi gian

khc. cc nt bin cha c chn lm nh ca hnh thoi ngi ta cn phi thay i s cht t (v d nh dng s ca hnh thoi hay b qua khng tnh mt c trng cn thiu nt bin. . . ).

u im ca s hin l thut ton n gin, d lp chng trnh cho my tnh in t tin dng cho c h thng mng knh (sng) phc tp. Nhc im ca s hin l bc thi gian tnh ton b hn ch bi iu kin:

t = inf LW

(*)

tc l bc thi gian phi nh hn gii hn di ca khong cch thi gian truyn nh hng t mt ct ny sang mt ct khc.

S d c hn ch l v trong qu trnh tnh ton ta lun lun phm phi sai s (do chnh xc ca ti liu a vo, do thay th vi phn bng sai phn, do sai s ca my tnh c hn...). Nu s tnh cho cc sai s b tch lu v khuch i trong qu trnh tnh th s khng bn vng. Ngc li nu trong qu trnh tnh sai s ban u gim dn, cc sai s phm phi khng b tch lu li th s l bn vng. Ngi ta chng minh rng s tnh ch bn vng khi s tnh ton p ng Iu kin trn. 1. S n.

S sai phn n l sai phn m trong qu trnh tnh lp thi gian c t hai nt tr ln v cc c trng Q, y cn tm. Sau khi sai phn ho h phng trnh Saint venant ta ch c c hai phng trnh i s, trong lc n s ln hn hay bng 4. Tng h phng trnh ring r nh vy khng kn v ta khng th gii ngay tm cc hm n c. Ch khi sai phn ho theo s chn cho mi nt thi gian sau, kt hp vi iu kin bin, ta mi

42

c mt h kn v gii ng thi ra nghim Q, cho tt c cc nt lp thi gian sau.

Cc nt A, B nm lp thi gian trc, cc c trng y bit. Cc nt C, D nm lp thi gian sau, cc c trng y cn tm. ta thay o hm ring bng cc biu thc sai phn sau y:

( )

t tC B= + bA bD

t 1

( )

s s ssD C B sA= + 1 (**)

( ) Qt t tC A D BQ Q Q Q= + 1

( ) Qs s s

D C B AQ Q Q Q= + 1

y 0 , 1 v gi l cc h s thin lch ( c ngha l khi sai phn ho ta ly thin v pha cnh no ca hnh ch nht ABCD).

Thng ngi ta chn = 1/ 2 v cho s tnh lun lun bn vng ly > 1/ 2 ( tc l o hm theo s ly thin v thi gian sau).

Sai phn ho h phng trnh Saint Venant theo biu thc (**) ta c hai phng trnh i s vi 4 n C, QC, D, QD.

Nu on sng tnh ton chia lm n on nh bng n+1 mt ct th p dng s ny ta c 2n phng trnh i s. k c hai iu kin bien ta c tt c 2n+2 phng trnh. S nt lp thi gian sau l n+1, s n s l 2(n+1), va bng s phng trnh.

Gii h 2n+2 phng trnh ny ta c ng thi tt c cc c trng cn tm lp thi gian sau (li dng tnh cht ring ca h phng trnh ny trong mi phng trnh ch c mt 4 n s, ngi ta dng phng php kh ui ny gii ra nhanh chng v n gin hn).

Ch do h phng trnh Sant Venant l phi tuyn nn ni chung h phng trnh i s nhn c cng l phi tuyn. Do m phi kt hp cch gii h phng trnh i s tuyn tnh vi php tnh ng dn (tnh lp).

u im ca s ny l vi > 1/ 2, bc thi gian tnh ton t khng b hn ch, s lun bn vng.

Nhc im l thut ton phc tp, kh lp chng trnh cho my tnh

43

in t hn, v khi p dng cho mng li knh (sng) th rt phin phc. Trong phi gii phng trnh sai phn cho tt c cc on knh ng

thi, mi c th tm c cc yu t thu lc cc nt.Ta nghin cu s n trc, v trong vic chuyn t phng trnh vi phn sang phng trnh sai phn rt t nhin v logic, tuy cch gii s c phn phc tp hn s hin.Trong sai phn y, chng ta s ly lu lng Q v mc nc Z lm hm s n. Ch : trong s sai phn to ca nt c xc nh l gi tr lu lng Q v din tch mt ct . Ta c th thay to bng (Q,z) v c quan h vi z.

Hnh 2.3- S sai phn hnh thoi. S

Hnh 2.4-S sai phn n hnh ch nht.

S

t t

s

s

C

B

D

A

O t

t

B

A C

D

s

44

2.3.3 H s trng lng ca s n Phng php sai phn trong s n gii phng trnh Saint Venant

l mt tin b ln. N c th dng gii cho cc bc thi gian kh di (1h) v di hn

Ux

ij

ij

xU U U Uij ij= +

+ + +11 1 1 1( )

= 't

t

= 0, im M ng j th l hon ton s n = 1 im M ng (j+1) l hon ton s hin.(Xem hnh 2.3) V

Ut

ij

ij

ij

ijU U U U

+ =+ + + + +1 1 1 1

2

_

2.3.4 Phng trnh c bn vit vi hm s n Q,Z trong trng hp tng qut. Ta vit li h phng trnh Saint Venant ly hm n l lu lng Q v

mc nc Z (cao vi mt chun c nh nm ngang) trong trng hp tng qut.

Khi vit quan h gia lu lng Q v lu tc trung bnh ca mt ct V di chuyn t h phng trnh (2.1, 2.4, 2.5) sang dng ny, ta cn ch trng hp nhng knh thng vi nhng khu cha nc ven b, nc coi nh khng chy, nhng mc nc thay i theo mc nc ca dng knh. Trong trng hp ny, lu tc trong hnh ca mt ct V ch tnh cho phn mt ct ngang ca dng chy V, k c bi su, trn lu tc c th phn b khng di (cc h s hiu chnh o v c th ln hn 1 mt cch ng k) phn mt ct ngang ny c chiu rng l B. Trong khi din tch mt ct tham gia phng trnh lin tc o phi k c khu cha, v chiu rng mt ct k c khu cha l Bo (xem hnh 2.4).

Nh vy phng trnh lin tc (2.4) vit l:

QS t

QS

BcgZ

tq+ = + = ' ( . )2 24

45

Trong phng trnh ng lc cc s hng

o

gVt

og

V VS

, c bin i

nh sau: Hnh 2.5 S sai phn.

Hnh 2.6 Mt ct ngang sng

h

Bc

B

B

Khong cch cchS

gian

1 2 3 4 i-1 i i+1 i+2 N-2 N-1

j+1 j

46

og

Vt

og t

Qg

Qt g

Qt

og

QT g

QB zT

o o

o

= =

=

2

2

g V

VS g

Qs

Qg

Q QS g

QS

= = 2

2

3

Ring trng hp knh lng tr th s hng

g

QS

2

3 cn c th vit l

= =

g

QS

Qg

B hS

Fr hS

2

3

2

3

Trong Fr l h s F rt. Phng trnh ng lc (2.11) s vit thnh

ZS g

Qt g

QBZt g

QS

Qg S

Q QK

o o Q+ +

=

2 2

2

3 2 2 25| |

( . )

Nu rt QS

t phng trnh lin tc (2.24)

QS

q Bc Zt

= ' V thay vo (2.25) s c

ZS g

QQt

B Bg

QZt

Qg

qg

QS

Q QK

o c o+ + +

=

2

2

2

232 26

.

'| |

( . )

Xt k hn na phng trnh ng lc, nu cho rng lng b sung dc

ng q' v lng nc i t khu cha tham gia dng chy (Bc - B) Zt

cng

i t ni c lu tc hng dc bng khng gia nhp dng chy ang c lu tc V1 th trong phng trnh ng lc phi k n phn nng lng cn ly t dng chnh a khi lng tham gia vo dng chy ca (2.26) phi a thm s hng.

47

q Bc B Zt

Vg

' ( _ )

Tuy nhin thc t dng chy b sung i t b hoc t khu cha khng phi l t ch lu tc hng dc hon ton bng khng ri ngay vo dng chy dng c lu tc hiu chnh j < 1.

Nh vy, phng trnh ng lc trong trng hp tng qut l:

ZS g

Qt

Bc Bg

QZt

jg

xQq

Qg S

j Bc Bg

QZt

Q QK

o o+ + + +

=

. . '

( ) | |( . )

2 2

2

3 2 2 2 27

Trong v tri, ni chung s hng th nht l quan trng nht ri ln lt n s hng th 2 v s hng th 3. Tu trng hp c th c th b qua 1 trong 3 s hng cui ca v tri. Chng hn khi lu lng b sung q' nh th b qua s hng th 4, khi lu tc trong knh nh so vi tc truyn sng (s

Frt Fr = Q Bg

2

3 rt nh so vi 1) th c th b qua s hng th 5. Tri li khi

dng chy l chy xit hoc gn bng trng thi phn gii (s Fr ln hn hoc

gn bng 1) th s hng th 5 -

Qg S

2

3 . li tr thnh quan trng khng th b

qua c. Hnh 2.7 S sai phn n.

t

3 2 1 0

S1 1 S2 2 n-1 n

48

Tuy nhin phn sau, chng ti s b qua s hng th 6 l s hng thng nh nht trong v tri, v cho j = 0 trong s hng th 4 din gii phng php sai phn. Nh vy phng trnh tng qut c dng vn l 2.26.

Trng hp ring khi tnh theo trng thi tc thi th b qua s hng th 2 v s hng th ba ca v tri, khi c th b qua lun c s hng th 4 v s th 5 cho tin, v phng trnh ng lc tnh trong trng thi tc thi ch cn

ZS

Q QK

= | | ( . )2 2 28

2.3.5 S sai phn n 1. Cng thc sai phn chia knh thnh tng on ngn S sao cho mi

on c cc c trng mt ct: , B, Bc, n... tng i u n, bin i t t, v khng c knh ngn, ln chy vo, c th c cc nhnh rt nh coi nh lu lng phn b dc ng q' - cc on c th di ngn khc nhau. Ta chia thi gian thnh nhng thi gian t (di bng nhau cho tin)

Ta c li sai phn nh hnh (2.5) Bit cc yu t thu lc Q,Z ti cc mt ct lc ban u (ti cc nt ca

hng th nht t = 0) ta s dng cc phng trnh s tnh ra cc tr s Q, Z ti mt ct cui thi on (cc nt hng th 2 t = 1t)... ln lt ta s tnh c Q v Z li tt c cc nt trn li.

tin theo di, ta k hiu cho mi yu t thu lc ti mi nt 2 ch s i, j nh Qij, Zij...

Ch s th 1 ch v tr mt ct i = 1, 2, 3,... n Ch s th 2 ch thi im j = 1, 2, 3, ... on knh t mt ct th (i - 1) n mt ct th (i ) gi l on knh

th i (hnh 2.5 ). Ta vit cc o hm ring ca mt i lng F no ra dng sai phn

nh sau: Xt on knh [(i-1), i] v thi on [(j-1),j] (Xem hnh 2.8 )

Ta c th thay Ft

bng

49

[ ]

Ft t

F j Fij Fi j Fi j

F j F jt

Fi j Fi jt

i

i i

+ + =

+

12 2

12

2 29

1 1 1 1

1 1 1 1

, ,

, , , ,( . )

Mt cch tng qut hn, cng c th sai phn ha Ft

cho on

(i-1,j)thin v u trn (i-1) hoc thin v u di (i), ngha l ly Ft

VFi j Fi j

tFi j Fi j

t + +( ) , , , , ( . )1 1 1 1 1 2 30

Vi 0 < V < 1

Ly = 1 tc l ly Ft

u di (mt ct i). Ly = 0 tc l ly Ft

u trn (mt ct i - 1).

Ni chung ly = 12

tc l dng cng thc (2.24) l hp l nht. Sau

ny ta s sai phn ha Qt

v ZT

theo (2.29)

Cng nh vy, ta sai phn ha FS

bng:

FS

=( ) , , , , ( . )1 2 311 1 1 1 + Fi j Fi jS

Fi j F jS

i

Vi 0 < < 1 Ly = 0 tc l thay o hm ring

FS

li tnh ton bng o

hm theo S vo lc u thi on (j-1) tri li, ly = 1 tc l thay o hm ring

FS

li tnh ton bng o hm theo S vo lc cui thi on (j).

Hnh 2.8

kt qu tnh vi =11/2 ng

trung

Q

t

50

Trc quan ta thy rng ly = 12

l lgic hn c; tuy nhin, theo l lun

phng php tnh cng nh theo kinh nghim tnh ton ly = 12

khng hn

dn n kt qu tnh bng s st nht vi nghim ng ca h phng trnh o hm ring v cc kh nng hi t.

Trong mt s sai phn c th ly cho QS

trong phng trnh lin tc

v cho ZS

trong phng trnh ng lc 2 tr s 1 v 2 khc nhau.

Trong phng trnh lin tc (2.4) nu ta sai phn ha QS

vi = 12

th

hp l nht, tuy nhin nghim tnh ra s b giao ng quanh tr s trung bnh nh hnh (2.8).

Khi tnh xong tr s Q, Z ca cc thi on ta cn hiu chnh li, bng cch ly kt qu theo 1 ng cong trn trung bnh.

i vi phng trnh ng lc (2.28) sai phn ha Zt

, nht thit

phi ly 2 > 12 . Tr s 2 = 12

l gii hn di ca s s dng ca nghim.

Kinh nghim tnh ton cho thy rng nu ly 2 khong 2/3 1 (sai phn ha Zt

vi 2 = 1 tc l ly dc mc nc tc thi, lc cui thi on t = j). Di y s trnh by cc cng thc so vi 1 2 1= = _Trong phng

trnh lin tc sai s ho ztt

theo 2.32 v sai phn ho.

Qij Qi jS

Bct

xZij Zi j Zi j Zi j

q t + +

=

1 12

1 1 12

2 32 , , ,

' ( . )

Trong : Bc: Chiu rng mt nc k c khu cha, ly trung bnh trn on knh v cng vi mc nc lc gia thi on, tc l ly trung bnh 4 im.

Trong thc t, khu cha bao gm bi cn b knh c thng vi mt nc knh, mc nc c th ln xung t do theo mc nc knh, trao i nc t do vi dng knh nhng lu tc hng dc khng ng k.

Ta gi tng din tch mc nc khu cha ni trn trong phm vi on

51

knh tnh ton l c, c ; l hm ca mc nc trung bnh ca on knh (xem hnh 2.9).

Hnh 2.9 S on knh c khu cha.

Theo ngha ca phng trnh lin tc, tr s B trong cng thc (2.32) phi tnh bng:

Bc BCS

= + (2.33)

Trong : B chiu rng trung bnh ca dng dn ng vi mc nc

trung bnh ca thi on Z

c din tch khu cha trong phm vi on knh ng vi mc nc trung bnh ca thi on Z (trong hnh 4 im)

Z = 14 1 1 1 1

( , , , , )Z j Z j Zi j Zi ji i + + + (2.34)

By gi ta tm cng thc sai phn cho phng trnh ng lc vi 2 = 1. V tuyn tnh ha phng trnh sai phn sau ny c th thay gii phng trnh o hm ring phi tuyn bng vic gii h phng trnh i s tuyn tnh, nn y ta cn mt s th thut tnh ton.

Trong phng trnh ng lc (2.28) cc o hm theo thi gian c sai phn ha theo kiu (2.29) cn cc h s ca n th ly trung bnh 4 im,

B

khu cha i-1

i

Bc

52

c th l:

og

Qt

og t

Qi j Q j Qi j Q j

Bc oBg

Q Zt

Bc oBg

Qt

x

Zi j Zi j Zi j Zi j

i i

+ +

+ +

+ +

12 2

1

12

1 1 12

1 1 1 1

2 2

, , , ,

, , , ,

Trong : aog

aBc aoBg

Qx

+

; 2

Coi l cc h s v ly trung bnh 4 im (k hiu 2 gch trn u).

Cn cc o hm theo S nh ZS

, g

QS2

cng vi cc s hng

Q QK

qg

Q| | , '2 2 . Th y ly lc t = j (tc 2 = 1)

ZS

Zi j Zt jS

Q QK

QK

Qi j Qi j

Qg S

Qg

i j i jS

Qi j Qi j

j

j

+

+

, ,

| | | | . , ,

, , . , ,

1

12

1 12

2 2

2

2 3

Trong cc h s c dng ( ) u c ly trung bnh ca on knh vo lc cui thi on (t=j), gi tt l trung bnh 2 im sau.

Thay cc s hng bin i nh trn vo (2.28) ta c Zi j Zi j

So

g tx

x Qi j Qi j Qi j Qi j

Bc oBg

Q Zi j Zi J Zi j Zi i

Qg

x COi j COi jS

Qi j Qi j

qg

Qi j Qi j QK

Qi

j

j j

, ,

( , , , , )

( , , , , )

, , ( , , )

' ( , , ) | | (

+

+

+

+

+ +

+ + =

12

1

1 1 1 1

21 1 1 1

21 1

21

2

2

3

2 2

, , )j Qi j+ 1 (2.35)

53

vit(2.27) v (2.35) thnh mt h phng trnh i s tuyn tnh i vi cc i lng cn tm Qi,j; Qi-1,j; Zi,j; Zi-1,j ta nhn 2 v ca cc phng trnh vi S v t

d og

St

e Bc oBg

Q St

fr Qg

i i

j q Sg

k Q SK

Qi j Qi j SK

j

j

j

jj

=

= +

=

=

=

=

+

22 36

22 37

22 38

22 39

21

4240

2

2 1

2

2 2

( . )

( . )

( ) ( . )

' ( . )

| | | , , | ( )

Ri sp xp li ta c

Qi,j - Qi-1,j + Bc s

tz z

Bc st

z z q j si j i j i j i j2 21 1 1 1 + = + +

( ) ( ), , , ,

v

z z d Q Q e z z fr Q Q Q Q k Q Qd Q Q e z z

i j i j i j i j i j i j i j i j i j i j i j i j

i j i j i j i j

, , , , , , , , , , , ,

, , , ,

( ) ( ) ( ) ( ) ( )( ) ( ) + + + + + + + + + =

+

1 1 1 1 1 1

1 1 1 1 1 1

Sp xp li theo th t cc t s Qi-1,j; Zi-1,j; Qi,j; Zi,j ta c

+ + + =

= + +

Q jBc S

tZ j Qi j

Bc St

Zi j

Bc St

Zi j Z j q S

i i

i j

1 1

1 1 1

2 2

2

, , , ,

( , , )

54

Q je

k d frZ j Qi j

k d fZi j

d Qi j Q j e Zi j Z jk d fr

i i

i i

+ + + + +

+ + + +

++ + +

1 1

1 1 1 1 1 1

1

1 2

, , ,

,

( , , ) ( , ,

ABc S

t

Ck d fr

Dk d fr

M A Zi Z j q S

Nd Qi j Q j e Zi j Z j

k d fr

j i

i i

=

= + + +

= + + +

= + + +

= + ++ + +

22 41

1 22 42

1 22 43

2 44

2 45

1 1 1

1 1 1 1 1 1

( . )

( . )

( . )

( , , ) ' ( . )

( , , ( , , )( . )

Ta c h phng trnh i s tuyn tnh tnh Q v Z l t = j -1Qi-1 + Ai Zi-1+1Qi+Ai Zi = Mi 1Qi-1 + Ci Zi-1 + 1Qi+Di Zi = Ni (2.46) Trong ( 2.46) cc n s u vo lc cui thi on t=j; t y tr i,

cho gn ta khng ghi ch ch s j na. Cc yu t lc u thi on (t=i-1) u c a sang v phi, coi nh bit.

Cn nhc li rng trong cc h s A, C, D.., cc i lng Bc, d, e phi ly trung bnh 4 im, cn cc i lng k, , fr th ly trung bnh 2 im lc cui thi on. Nh vy cc h s ca phng trnh li ph thuc n s cn tm Q, Z lc t = j. Ta phi gii quyt iu bng thut ton tnh lp, c th l: ln u tm tnh cc h s theo cc yu t bc u thi on t=j-1 (l cc yu t bit) da vo phng trnh v gii ra c cc nghim s gn ng ln th 1; t s tnh li cc h s ri a vo phng trnh gii ln

55

th 2 tm nghim s ng hn. C lm nh th cho n khi kt qu hai ln tnh lp lin tip ch cn sai khc nhau nh hn sai s cho php l c. -Gi s Q, Z l sai s cho php v lu lng v mc nc, khi tnh lp n ln th k, c Qk, Zk ta dng cc tr s tnh li cc h s ca h phng trnh ri gii li ln th kt1, ta c Qkt1, Zkt1.

Nu thy: |Qk - Qkt1| Q |Zk - Zkt1| Z (2.47) c th coi l c. Vi cch tnh lp ni trn, trong mi ln tnh ta u coi cc h s A,

C, D, M, N l cc hng s bit. By gi ta nghin cu cch gii cc phng trnh i s bc nht ( 2.46). Mi h phng trnh (2.46) thuc on th i l 2 phng trnh v cha

4 n s: Qi-1, Zi-1,Qi, Zi. Ton knh cn tnh ton c chia thnh n on, t mt ct 0-0 n

mt ct n-n, mi on c 2 phng trnh (2.46), tt c c 2n phng trnh i s tuyn tnh, sp xp li nh sau:

on 0-1: -1Qo +A1Zo + 1Q1 + A1Z1 = M1 + 1Qo + C1Zo + 1Q1 + D1 Z1 = N1 on 0-2: -1Q1 + A2Z1 + 1Q2 + A2Z2= M2 -1Q1 + C2Z1 + 1Q2 + D2Z2= N2 (2.48) on n-1,n: -1Qn-1 + AnZn-1+1Qn+AnZn=Mn +1Qn-1 + CnZn-1+1Qn+DnZn=Nn Ta phi tm tt c (2n + 2) n s Q v Z ti (n + 1) mt ct. Cn kt hp

2n phng trnh (2.42) vi 2 iu kin hai u. Gi s iu kin cho l: "bit ng qu trnh lu lng u trn v ng qu trnh mc nc u di", tc l bit Qo v Zn, ta s cn li 2n n s l Zo, Q1, Z1, Q2,... Zn-1, Qn, lc h (2.42) gii. Hai iu kin t nhin 2 u cng c th cho di dng phng trnh quan h Qo = t (Zo) hoc Qn = f (Zn), cng vi (2.42), cng thnh 1 h 2n+2 phng trnh gii ra 2n+2 n.

56

Ta thy rng vi s sai phn ny, khng th ch dng h phng trnh sai phn c bn ca 1 on tm ra Q, Z ca on , m phi gii ng thi nhiu phng trnh ca tt c cc on cng vi iu kin mi tm c nghim. Do gi l s n.

Gii h phng trnh nhiu n nh th tt nhin i hi mt khi lng tnh ton rt ln, mc d cc ma trn cc h s ca cc phng trnh trn c nhiu s hng bng khng. ng thi, li phi gii h phng trnh n nhiu ln do phi tnh lp hiu chnh cc h s.

Chnh do khi lng tnh ton qu ln, nn trc y khi cha c my tnh in t, ngi ta khng th dng c phng trnh y nh trn gii cc bi ton v dng khng n nh. Trong cc trng hp dng chy m v c s bin ng khng mnh lm, ngi ta c th b qua hai s hng

o

gvt

v g VvS

, khi phng trnh ng lc rt v phng trnh vi phn

ca dng khng u tc thi, v phng php ny gi l phng php tc thi.

Trong trng hp ring ny, l lun v cc cng thc sai phn hon ton nh trn, h phng trnh (2.46 v 2.48) khng c g thay i. Ch khc l cc h s c n gin i, do b qua cc i lng cha o v tc l trong cc cng thc (2.41 n 2.45 ) ta u cho:

e = d = fr = = 0 Do :

Ck

kQ S

Dk

kQ S

N

= =

= =

=

1 22 49

1 22 50

0 2 51

2

| |( . )

| |( . )

( . )

Cn A, M khng c g thay i y xem phng php trng thi tc thi nh mt trng hp ring

ca phng php sai phn bng s n, cch gii c th nh trng hp tng qut.

57

2.3.6 Cch gii bng kh ui H phng trnh i s tuyn tnh nhiu n nhng ch c t h s khc

khng sp xp nh (2.48) c th c gii bng 1 s phng php ring nhanh hn trng hp phng trnh y : trong s cc phng php .Cc phng php kh ui l mt phng php kh thun tin.

1) Cch gii kh iu kin bin u trn cho Qo ta t: Qo=P0z0+q0 on 0-1: Zo = Q1 + o Q1 = P1Z1+q1 (2.52) on 1-2: Z1 = 1 Q2+1 Q2 = P2Z2+q2 on n-1,n: Zn-1 = n-1Qn +n-1 Qn = Pn Zn + qn , , P, q gi l h s kh ui V Qo u cho trc, khng ph thuc Zo,nn u tin ta cho: qo = Qo Po= 0 Ta dng h phng trnh (2.4.6) ca on 0-1 tnh o, o, P, q -1Qo+A1Zo+1Q1+A1Z1 = M1 +1Qo+C1Zo+1Q1+D1Z1 = N1 Bit P1, q ta li dng h phng trnh thuc on 1-2 tnh , 1,p2,

q2... Tng qut bit Polime-1, qi-1 ta s dng phng trnh on (i-1, i) tnh i-1, i-1, p1,q1 bng cch bin i cng thc ( 2.46) nh sau:

-1Qi-1 + A1.Zi-1 + 1.Qi +AiZi = Mi -1Qi-1 + C1.Zi-1 + 1.Qi +DiZi = Ni Kh Z1 bng cch nhn phng trnh th 1 vi D1 v phng trnh th

2 vi A1 ri cng li ta c. D1.Qi-1 - D1 A1.Zi-1 -D1.Qi - D1.AiZi = -D1.Mi Ai.Qi-1 + C1 .A1.Zi-1 + A1.Qi +Di A1.Zi = A1.Mi

58

(Ai + Di).Qi-1 + Ai(Ci - Di).Zi-1 + (A1 - D1) = Ai.Ni - Di.Mi Ri kh Qi-1 bng cch thay Qi-1 = Pi-1.Zi-1 + qi-1 vo phng trnh trn

v sp xp li ta c:

Zi-1 = D A

A D P A C DQ

A N D M A Di qAi Di P Ai Ci Di

i i

i i i i i ii

i i i i i i

i

+ + +

++ +

( ) ( )

. ( )( ) ( )1

1

1

ng nht vi: Zi-1 = i-1 Q1 + i-1 Ta c

i-1 =C

kk

Q S

Dk

kQ S

N

= =

= =

=

1 22 4 9

1 22 5 0

0 2 5 1

2

| |( . )

| |( . )

( . )

(2.53)

i-1 = AiNi DiMi Ai Di qA D P A C D

i

i i i i i i

++ +

( )( ) ( )

1

1 (2.54)

By gi ta tnh Pi v qi, ta li kh Qi-1 bng cch cng hai v ca (2.46) vi nhau c: (Ai + CiZi-1 + 2Qi + (Ai + Di)Zi = MiNi Kh Zi-1 bng cch thay Zi-1 = i-1Qi + i-1 vo phng trnh trn v sp

xp li, nh sau:

Qi = ++ ++ +

+ +

( )( )

( )( )

Ai DiAi Di

ZiMi Ni Ai Ci

Ai Diii

i

11

12 2

ng nht vi Qi = PiZi + qi Ta c:

Pi = ++ +( )

( )Ai Di

Ai Dii 1 2 (2.55)

Qi = Mi Ni Ai Ci

Ai Dii

i

+ ++ +

1

1 2( )

( ) (2.56)

C nh th, bt u t P0 = 0, q0 = Q0 ta tnh 0, 0, P1, Q1, 1,P2, Q2, ..., n-1, Pn, qn.

Sau ta s s dng iu kin bn di tnh ngc tr li theo cc cng thc (2.52) a ra cc tr s Qi v Zi.

Gi s bn di cho Zn, ta tnh ngay c Qn = PnZn + qn ri t Qn tnh sang Zn-1 = n-1Qn + n-1

59

Nu bn di cho quan h Qn = f(Zn) th s tnh ra Qn, Zn bng giao im ca ng cong Qn = f(Zn) vi ng thng Qn = PnZn + qn, xem hnh (2.8) sau tnh ln Zn-1, Qn-1...

2) Cch gii khi iu kin bin u trn cho Z0 Z0 = Q0 + V0 on 0 - 1

Q t Z SZ Q V

0 0 0 0

1 1 1 1

= += +

on 1 - 2Q t Z SZ Q V

1 1 2 1

2 2 2 2

= += +

(2.57) ...

on n - 1 Q t Z SZ Q V

n n n n

n n n n

= += +

1 1

Hnh 2.10 Cng lm tng t nh trn ta c th t i-1, -1, suy ra t ti-1, Si-1 v i,

i bng phng trnh (2.46) ca on (i-1, i). Tr hai v ( 2.46) ta kh c Qi.

2Qi-1 + (Ci - Ai) Zi-1 + (Di - Ai) Zi = Ni - Mi Thay Zi-1 bng i-1Qi-1 + Vi-1 v sp xp li ta c:

Q t Z SZ Q V

1 1 2 1

2 2 2 2

= += +

ng nht vi

Qn=pZn+qn

Q(n)=f(Zn)

Zn

Qn

60

Qi-1 = ti-1Zi + Si-1

Ta c: t Ai DiAi Cii i

= 1 12 ( ) (2.58)

Si-1 = Q t Z SZ Q V

0 0 0 0

1 1 1 1

= += +

(2.59)

By gi nhn phng trnh th nht ca (2.4.6) vi C v nhn phng trnh th 2 vi A ri cng li ta s kh c Zi-1. Sau thay Qi-1 bng ti-1Zi + Si-1 v sp xp li ta c:

Zi = Ci AiAi Ci t Ai Di Ci

Qi AiNi CiMi Si Ai CiAi Ci t Ai Di Cii i

+ + +

++ + ( ) (

( )( ) (1 1

ng nht vi Zi = iQi + Vi Ta c:

i = M i N i A i C iA i D i

i

i

+ ++ +

1

1 2( )

( ) (2.60)

Vi = AiNi CiMi S Ai Ci

Ai Ci t Ai Di Cii

i

++ +

1

1

( )( ) ( )

(2.61)

Theo cng thc trn xut pht t: 0 = 0 V0 = Z0 (iu kin nu trn) Ta s ln lt rt ra t0, S0 1, V1 bng cc i lng A, C, D, M, N ca

on (0 - 1) ri tnh c t1, S1 2, V2 ca on (1, 2)... c nh th cho n n, Vn.

Sau ta s i t iu kin trn mt ct cui m tnh ra cc gi tr s Q v Z, ngc t di tr ln, theo cc cng thc (2.57), t Qn, Zn.. .n Z1, Q0, Z0...

Cc trng hp cho iu kin lun khc cng tng t nh trn. Tt nhin ta cng c th tnh cc h s kh ui t di tr ln, ri tnh

ra nghim Q, Z t u trn ca knh tr xung. Chng ta c th theo ng li trn m lp cc cng thc tnh cho cc trng hp c th khc.

Khi s dng phng php kh ui, cn ch rng n i hi mc chnh xc kh cao ca cc php tnh, v thng thng cc p s Q v Z tnh theo (2.52) hoc (2.57) l tng ca 2 s hng khc du. Mun cho tng t

61

n mt sai s tng i nh hn k101 th n khi i hi mi s hng ca

tng phi c mt sai s tng i nh hn 110 2k+

.

Nh vy, ta thy rng mun cho p s Q ng n con s c ngha th k th phi ly Pn, qn ng n con s c ngha th k + 2 hoc k + 3.

2.4. S lc v hi t v s n nh ca nghim Trong vic tnh nghim bng s theo phng php sai phn , ta thay

cc o hm ring 110 2k+

bng tng s cc gi s

F

S

F

t. , nghim tnh

c ch l gn ng. C th ngh rng khi cho cc on chia S v t cng nh th nghim

tm ra s cng tin ti nghim ng ca phng trnh vi phn. Nhng thc ra khng hn nh vy, nghim bng s tm c bng phng php sai phn ca hi t v nghim ng ca phng trnh vi phn khi cho S, t tin ti v cng nh, vi iu kin trn s tnh ton c t s

tS thch ng v c

cch thay i thch ng cc o hm bng t s sai phn hu hn v c cch ly thch ng cc h s. Trong trng hp s cn tnh ton mi hi t. Tri li nu s tnh ton khng nhng iu khon cn thit nht nh th d ta cho s, t rt nh, nghim tnh ra cng khc xa vi nghim ng ca phng trnh vi phn.

Mt khc, trong vic tnh ton bng s ta khng trnh khi sai s do ly trn s. Khi tnh sai phn t mt ct ny sang mt ct khc, nu sai s mt bc tnh ton no c b khuych i mi ln, v cng tnh nhiu bc sai s cng ln ln, th s tnh ton c gi l khng n nh.

Trong trng hp , nu chn on s, t cng nh s bc tnh cng nhiu ln, th nghim tm c s cn khc vi nghim ng ca phng trnh vi phn .

Tri li, nu sai s mt bc tnh ton no y khng gy ra sai s ln hn cho bc tnh sau - hoc cc sai s trong cc php tnh trung gian b tr nhau, th sn phm l n nh.

Nghin cu tch hi t v n nh ca nghim l mt vn phc tp

62

ca phng php tnh. y khng i su phn tch l lun ca vn ny. Xt trn s sai phn n v gii thiu trn, ch cn nu ln vn tnh n nh v hi t ca s ph thuc ch yu vo h s 1 v 2 chn sai phn ho cc o hm

QS

v SZ . S s m bo n nh v hi t nu ly

1>1/2, 2>1/2 v ly h s v phi tng ng. S c chn v trnh by trn ( vi 1= 2=1 v Q Q

K2 ly

trung bnh 2 nu lp sau ng vi 2=1) m bo tnh n nh v hi t. S hi t ca s sai phn nh va nh ngha trn khc vi s hi

t ca php tnh lp khi xc nh cc h s, tuy hai vn d c lin quan vi nhau. Vi mt quy nh no v cch ly cc h s ( chng hn nh y ta quy nh: yu t d v e ly trung bnh 4 im, yu t k v tr ly trung bnh 2 im lp sau ) th phi gii bi ton vi bng nhiu tnh lp, cho n khi tho mn iu kin (2.47) mi c.

Trn c s tn trng nhng iu quy nh ni trn, php gii s hi t nhanh hay chm, tc c ngha l phi qu t hay nhiu ln lp mi tho mn iu kin (2.47), iu cn ph thuc vo s kho lo ca thut ton. Thut ton tnh lp thch ng s rt ngn c khi lng ton. Khi chn thut ton cn ch hai trng hp c th xy ra :

a, Nghim s F tm ra cc ln tnh lp lin tip din ra theo kiu hnh (9a) tc l khi :

Fk+1 - Fk 1/2Fk - Fk+1

Hnh 2.11a

FK-1 FK+1

FK+2

63

Hnh 2.11b Khi gii bi ton gp trng hp th 1 hoc trng hp th 2 l tu

theo cch sai phn hoc ca s , mi trng hp phi chn mt thut ton li nht.

Trong trng hp 1, th ly chnh Fk lm nghim s hiu chnh cc h s cho ln th lp k+1

Trong trng hp 2, sau khi tnh xong ln th k tm c Fk th li

nn coi Fk Fk +12 l nghim s hiu chnh cc h s cho ln tnh lp th k+1,

nh th s chng t n (2.47) hn (s ln tnh lp t hn).

2.5 S sai phn hin tnh ton cho knh h. C nhiu kiu s sai phn hin di y gii thiu s tnh ton

hnh thoi.

2.5.1. S v cng thc c bn. tin din gii ta hy xt mt knh n khng r nhnh khng c

cng trnh trn knh, vi iu kin bin l: cho bit ng qua trnh lu lng n trn ( s=0) v ng qu trnh mc nc u di. (S=1)

Qo = Qo (t) Zl = Zl (t) Chia chiu di knh ra nhiu on nh s di u nhau, v nh s cc

mt ct chia on 0,1,2,3... theo chiu dng ca trc S vi quy c lu lng l (+) khi chng theo chiu (+) ca S. Ta cng chia thi gian thnh nhng thi on t di u nhau, nh s cc thi im 0,1,2,... nh vy mt phng (s,t) c chia thnh li ch nht (hnh 5-10), mi nt ca li c nh s bng 2 ch s (, ); ch s th 1 i, , ch s th 2j, ch thi im.

FK-1 FK+1 FK+2 FK FK-1

FK

64

Trn li ta quy nh : s tnh mc nc Z ti cc nt l v thi im l nh du X trong hnh (2.12) v tnh lu lng Q cho cc nt cc mt ct chn vi thi im chn (nh s 0 trong hnh 2.12). Do , nu iu kin trn cho lu lng u trn v mc nc u di th phi nh s mt ct u trn knh l mt ct s 0 v mt ct cui knh l mt s l 2n+1. Ngc li, nu iu kin trn cho mc nc 2 u th phi nh s mt ct u trn knh l s 1, ngha l tng s nh l mt s chn.

Hnh 2.12 S tnh.

Hnh 2.13

...

4 3 2 1 0 -1

1 2 3 2i-2 2i 2i-1 2i+1

2n 2n+1

...

t

S

0 1 2 3 S

t 2 1 0 -1

1

0

65

Theo iu kin ban u, ta bit mc nc tt c cc mt ct l, thi im t = -1 v bit lu lng tt c cc mt ct chn, thi im t = 0. Ta s tnh mc nc ti tt c cc mt ct l, thi im t = +1 bng phng trnh lin tc.

Xt mt hnh thoi c 4 nh hnh 2.13 l cc nt (1, -1) (0,0), (2, 0), (1,1) bit Z1,1, Q0,0, Qz, 0 ta tnh ra Z1,1 bng phng trnh lin tc, sai phn ho nh sau:

Q QS

BZ Z

tq q

C2 0 0 0

1 01 1 1 1 0 2

2 2 2, ,

,, , ' ' + = +

l cng thc sai phn theo kiu sai phn trung tm, rt trng ngha ca o hm ring, h s BC phi ly mt ct gia, theo mc nc

trung bnh (tc t = 0) Z1,0 = Z Z1 1 1 1

2,